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Orgest Zaka - One of the best experts on this subject based on the ideXlab platform.
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skew field of trace preserving endomorphisms of translation group in Affine Plane
Proyecciones (antofagasta), 2020Co-Authors: Orgest Zaka, Mohanad A MohammedAbstract:We will show how to constructed an Skew-Field with trace-preserving endomorphisms of the Affine Plane. Earlier in my paper, we doing a detailed description of endomorphisms algebra and trace-preserving endomorphisms algebra in an Affine Plane, and we have constructed an associative unitary ring for which trace-preserving endomorphisms. In this paper we formulate and prove an important Lemma, which enables us to construct a particular trace-preserving endomorphism, with the help of which we can construct the inverse trace-preserving endomorphisms of every trace-preserving endomorphism. At the end of this paper we have proven that the set of tracepreserving endomorphisms together with the actions of ’addition’ and ’composition’ (which is in the role of ’multiplication’) forms a skewfield.
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the endomorphisms algebra of translations group and associative unitary ring of trace preserving endomorphisms in Affine Plane
Proyecciones (antofagasta), 2020Co-Authors: Orgest Zaka, Mohanad A MohammedAbstract:A description of Endomorphisms of the translation group is introduced in an Affine Plane, will define the addition and composition of the set of endomorphisms and specify the neutral elements associated with these two actions and present the Endomorphism algebra thereof will distinguish the Trace-preserving endomorphism algebra in Affine Plane, and prove that the set of Trace-preserving endomorphism associated with the ’addition’ action forms a commutative group. We also try to prove that the set of trace-preserving endomorphism, together with the two actions, in it, ’addition’ and ’composition’ forms an associative and unitary ring.
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the endomorphisms algebra of translations group and associative unitary ring of trace preserving endomorphisms in Affine Plane
arXiv: General Mathematics, 2020Co-Authors: Orgest ZakaAbstract:This paper introduces a description of Endomorphisms of the translation group in an Affine Plane, will define the addition and composition of the set of endomorphisms and specify the neutral elements associated with these two actions and present the Endomorphism algebra thereof will distinguish the Trace-preserving endomorphism algebra in Affine Plane, and prove that the set of Trace-preserving endomorphism associated with the 'addition' action forms a commutative group. We also try to prove that the set of trace-preserving endomorphism, together with the two actions, in it, 'addition' and 'composition' forms an associative and unitary ring.
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Ordered Line and Skew-Fields in the Desargues Affine Plane
arXiv: History and Overview, 2019Co-Authors: Orgest Zaka, James F. PetersAbstract:This paper introduces ordered skew fields that result from the construction of a skew field over an ordered line in a Desargues Affine Plane. A special case of a finite ordered skew field in the construction of a skew field over an ordered line in a Desargues Affine Plane in Euclidean space, is also considered. Two main results are given in this paper: (1) every skew field constructed over a skew field over an ordered line in a Desargues Affine Plane is an ordered skew field and (2) every finite skew field constructed over a skew field over an ordered line in a Desargues Affine Plane in $\mathbb{R}^2$ is a finite ordered skew field.
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isomorphic dilations of the skew fields constructed over parallel lines in the desargues Affine Plane
arXiv: Metric Geometry, 2019Co-Authors: Orgest Zaka, James F. PetersAbstract:This paper considers dilations and translations of lines in the Desargues Affine Plane. A dilation of a line transforms each line into a parallel line whose length is a multiple of the length of the original line. In addition to the usual Playfair axiom for parallel lines in an Affine Plane, further conditions are given for distinct lines to be parallel in the Desargues Affine Plane. This paper introduces the dilation of parallel lines in a finite Desargues Affine Plane that is a bijection of the lines. Two main results are given in this paper, namely, each dilation in a finite Desarguesian Plane is an isomorphism between skew fields constructed over isomorphic lines and each dilation in a finite Desarguesian Plane occurs in a Pappian space.
Zaka Orgest - One of the best experts on this subject based on the ideXlab platform.
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Skew-Field of Trace-Preserving Endomorphisms, of Translation Group in Affine Plane
2020Co-Authors: Zaka OrgestAbstract:In this paper we will show how to constructed an Skew-Field with trace-preserving endomorphisms of the Affine Plane. Earlier in my paper, we doing a detailed description of endomorphisms algebra and trace-preserving endomorphisms algebra in an Affine Plane, and we have constructed an associative unitary ring for which trace-preserving endomorphisms. In this paper we formulate and prove an important Lemma, which enables us to construct a particular trace-preserving endomorphism, with the help of which we can construct the inverse trace-preserving endomorphisms of every trace-preserving endomorphism. At the end of this paper we have proven that the set of trace-preserving endomorphisms together with the actions of 'addition' and 'composition' (which is in the role of 'multiplication') forms a skew-field.Comment: 11 pages. arXiv admin note: substantial text overlap with arXiv:2003.0952
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The Endomorphisms Algebra of Translations Group and Associative Unitary Ring of Trace-Preserving Endomorphisms in Affine Plane
2020Co-Authors: Zaka OrgestAbstract:This paper introduces a description of Endomorphisms of the translation group in an Affine Plane, will define the addition and composition of the set of endomorphisms and specify the neutral elements associated with these two actions and present the Endomorphism algebra thereof will distinguish the Trace-preserving endomorphism algebra in Affine Plane, and prove that the set of Trace-preserving endomorphism associated with the 'addition' action forms a commutative group. We also try to prove that the set of trace-preserving endomorphism, together with the two actions, in it, 'addition' and 'composition' forms an associative and unitary ring.Comment: 10 page
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Isomorphic-Dilations of the skew-fields constructed over parallel lines in the Desargues Affine Plane
2019Co-Authors: Zaka Orgest, Peters, James F.Abstract:This paper considers dilations and translations of lines in the Desargues Affine Plane. A dilation of a line transforms each line into a parallel line whose length is a multiple of the length of the original line. In addition to the usual Playfair axiom for parallel lines in an Affine Plane, further conditions are given for distinct lines to be parallel in the Desargues Affine Plane. This paper introduces the dilation of parallel lines in a finite Desargues Affine Plane that is a bijection of the lines. Two main results are given in this paper, namely, each dilation in a finite Desarguesian Plane is an isomorphism between skew fields constructed over isomorphic lines and each dilation in a finite Desarguesian Plane occurs in a Pappian space.Comment: 15 pages, 6 figure
Mohanad A Mohammed - One of the best experts on this subject based on the ideXlab platform.
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skew field of trace preserving endomorphisms of translation group in Affine Plane
Proyecciones (antofagasta), 2020Co-Authors: Orgest Zaka, Mohanad A MohammedAbstract:We will show how to constructed an Skew-Field with trace-preserving endomorphisms of the Affine Plane. Earlier in my paper, we doing a detailed description of endomorphisms algebra and trace-preserving endomorphisms algebra in an Affine Plane, and we have constructed an associative unitary ring for which trace-preserving endomorphisms. In this paper we formulate and prove an important Lemma, which enables us to construct a particular trace-preserving endomorphism, with the help of which we can construct the inverse trace-preserving endomorphisms of every trace-preserving endomorphism. At the end of this paper we have proven that the set of tracepreserving endomorphisms together with the actions of ’addition’ and ’composition’ (which is in the role of ’multiplication’) forms a skewfield.
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the endomorphisms algebra of translations group and associative unitary ring of trace preserving endomorphisms in Affine Plane
Proyecciones (antofagasta), 2020Co-Authors: Orgest Zaka, Mohanad A MohammedAbstract:A description of Endomorphisms of the translation group is introduced in an Affine Plane, will define the addition and composition of the set of endomorphisms and specify the neutral elements associated with these two actions and present the Endomorphism algebra thereof will distinguish the Trace-preserving endomorphism algebra in Affine Plane, and prove that the set of Trace-preserving endomorphism associated with the ’addition’ action forms a commutative group. We also try to prove that the set of trace-preserving endomorphism, together with the two actions, in it, ’addition’ and ’composition’ forms an associative and unitary ring.
Samuel Boissiere - One of the best experts on this subject based on the ideXlab platform.
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chern classes of the tangent bundle on the hilbert scheme of points on the Affine Plane
Journal of Algebraic Geometry, 2005Co-Authors: Samuel BoissiereAbstract:SAMUEL BOISSI`EREAbstract. The cohomology of the Hilbert schemes of points on smooth pro-jective surfaces can be approached both with vertex algebra tools and equi-variant tools. Using the first tool, we study the existence and the structure ofuniversal formulas for the Chern classes of the tangent bundle over the Hilbertscheme of points on a projective surface. The second tool leads then to nicegenerating formulas in the particular case of the Hilbert scheme of points onthe affine Plane.
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chern classes of the tangent bundle on the hilbert scheme of points on the Affine Plane
arXiv: Algebraic Geometry, 2004Co-Authors: Samuel BoissiereAbstract:The cohomology of the Hilbert schemes of points on smooth projective surfaces can be approached both with vertex algebra tools and equivariant tools. Using the first tool, we study the existence and the structure of universal formulas for the Chern classes of the tangent bundle over the Hilbert scheme of points on a projective surface. The second tool leads then to nice generating formulas in the particular case of the Hilbert scheme of points on the Affine Plane.
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on the mckay correspondences for the hilbert scheme of points on the Affine Plane
arXiv: Algebraic Geometry, 2004Co-Authors: Samuel BoissiereAbstract:The quotient of a finite-dimensional vector space by the action of a finite subgroup of automorphisms is usually a singular variety. Under appropriate assumptions, the McKay correspondence relates the geometry of nice resolutions of singularities and the representations of the group. For the Hilbert scheme of points on the Affine Plane, we study how different correspondences (McKay, dual McKay and multiplicative McKay) are related to each other.
Ilia Ponomarenko - One of the best experts on this subject based on the ideXlab platform.
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on schurian fusions of the association scheme of a galois Affine Plane of prime order
Journal of Mathematical Sciences, 2020Co-Authors: Bahareh Asadian, Ilia PonomarenkoAbstract:The schurian fusions of the association scheme of a Galois Affine Plane of prime order are completely identified. Bibliography: 12 titles.
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on schurian fusions of the association scheme of a galois Affine Plane of prime order
arXiv: Combinatorics, 2019Co-Authors: Bahareh Asadian, Ilia PonomarenkoAbstract:The schurian fusions of the association scheme of a Galois Affine Plane of prime order are completely identified.