| 1. |
- Akbari, Saieed, et al.
(författare)
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Chromatic number and clique number of subgraphs of regular graph of matrix algebras
- 2012
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Ingår i: Linear Algebra and its Applications. - : Elsevier BV. - 0024-3795 .- 1873-1856. ; 436:7, s. 2419-2424
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Tidskriftsartikel (refereegranskat)abstract
- Let R be a ring and X subset of R be a non-empty set. The regular graph of X, Gamma(X), is defined to be the graph with regular elements of X (non-zero divisors of X) as the set of vertices and two vertices are adjacent if their sum is a zero divisor. There is an interesting question posed in BCC22. For a field F, is the chromatic number of Gamma(GL(n)(F)) finite? In this paper, we show that if G is a soluble sub-group of GL(n)(F), then x (Gamma(G)) < infinity. Also, we show that for every field F, chi (Gamma(M-n(F))) = chi (Gamma(M-n(F(x)))), where x is an indeterminate. Finally, for every algebraically closed field F, we determine the maximum value of the clique number of Gamma(< A >), where < A > denotes the subgroup generated by A is an element of GL(n)(F). (C) 2011 Elsevier Inc. All rights reserved.
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| 2. |
- Aryapoor, Masood, 1977-
(författare)
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Explicit Hilbert's Nullstellensatz over the division ring of quaternions
- 2024
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Ingår i: Journal of Algebra. - : ACADEMIC PRESS INC ELSEVIER SCIENCE. - 0021-8693 .- 1090-266X. ; 657, s. 26-36
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Tidskriftsartikel (refereegranskat)abstract
- Using the Rabinowitsch trick, we prove an explicit version of the central quaternionic Nullstellensatz formulated and proved by Alon and Paran. (c) 2024 The Author. Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).
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| 3. |
- Aryapoor, Masood, 1977-
(författare)
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Non-commutative Henselian rings
- 2009
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Ingår i: Journal of Algebra. - : Elsevier BV. - 0021-8693 .- 1090-266X. ; 322, s. 2191-2198
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Tidskriftsartikel (refereegranskat)abstract
- Non-commutative Henselian rings are defined and some basicproperties of them are discussed. It is shown that a local ringwhich is complete in the topology defined by its maximal ideal isHenselian provided that it is almost commutative. Some examplesof non-commutative Henselian rings are also given.
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| 4. |
- Aryapoor, Masood, 1977-, et al.
(författare)
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On uniformly generating Latin squares
- 2011
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Ingår i: Bulletin of the Institute of Combinatorics and its Applications. - 1183-1278 .- 2689-0674. ; 62, s. 48-58
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Tidskriftsartikel (refereegranskat)
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| 5. |
- Aryapoor, Masood, 1977-
(författare)
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Self-dual Yang-Mills equations in split signature
- 2010
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Ingår i: Advances in Mathematics. - : Elsevier BV. - 0001-8708 .- 1090-2082. ; 224:5, s. 2022-2051
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Tidskriftsartikel (refereegranskat)abstract
- We study the self-dual Yang Mills equations in split signature. We give a special solution, called the basic split instanton, and describe the ADHM construction in the split signature. Moreover a split version of t'Hooft ansatz is described.
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| 6. |
- Aryapoor, Masood, 1977-
(författare)
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Skew-convex function rings and evaluation of skew rational functions
- 2024
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Ingår i: Communications in Algebra. - : TAYLOR & FRANCIS INC. - 0092-7872 .- 1532-4125.
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Tidskriftsartikel (refereegranskat)abstract
- The product formula for evaluating products of skew polynomials is used to construct a class of rings. As an application, we present a method of evaluating quotients of skew polynomials.
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| 7. |
- Aryapoor, Masood, 1977-
(författare)
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The Penrose transform in split signature
- 2012
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Ingår i: Differential geometry and its applications (Print). - : Elsevier BV. - 0926-2245 .- 1872-6984. ; 30:4, s. 334-346
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Tidskriftsartikel (refereegranskat)abstract
- A version of the Penrose transform is introduced in split signature. It relates cohomological data on CP3 \ RP3 and the kernel of differential operators on M, the (real) Grassmannian of 2-planes in R-4. As an example we derive the following cohomological interpretation of the so-called X-ray transformH-c(1)(CP3\RP3, O(-2)) ->congruent to ker(rectangle(2.2) : Gamma(omega) (M, (epsilon|-1|) over tilde) -> Gamma(omega) (M, (epsilon|-3|) over tilde))where Gamma(omega) (M, (epsilon|-1|) over tilde) and Gamma(omega) (M, (epsilon|-3|) over tilde) are real analytic sections of certain (homogeneous) line bundles on M, c stands for cohomology with compact support and rectangle(2.2) is the ultrahyperbolic operator. Furthermore, this gives a cohomological realization of the so-called "minimal" representation of SL(4, R). We also present the split Penrose transform in split instanton backgrounds.
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| 8. |
- Saieed, Akbari, et al.
(författare)
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On linear transformations preserving at least one eigenvalue
- 2003
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Ingår i: Proceedings of the American Mathematical Society. - 0002-9939 .- 1088-6826. ; 132:6, s. 1621-1625
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Tidskriftsartikel (refereegranskat)abstract
- Let F be an algebraically closed field and T : Mn(F) −→ Mn(F)be a linear transformation. In this paper we show that if T preserves atleast one eigenvalue of each matrix, then T preserves all eigenvalues of eachmatrix. Moreover, for any infinite field F (not necessarily algebraically closed)we prove that if T : Mn(F) −→ Mn(F) is a linear transformation and for anyA ∈ Mn(F) with at least an eigenvalue in F, A and T(A) have at least onecommon eigenvalue in F, then T preserves the characteristic polynomial.
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