Results 11 to 20 of about 386,457 (283)
The matrix Jacobson graph of finite commutative rings
Electronic Journal of Graph Theory and Applications, 2022 The notion of the matrix Jacobson graph was introduced in 2019. Let R be a commutative ring and J(R) be the Jacobson radical of ring R. The matrix Jacobson graph of ring R size m × n, denoted 𝔍(R)m × n, is defined as a graph where the vertex set is Rm ...
Siti Humaira +3 more
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Homomorphisms of matrix rings into matrix rings [PDF]
Pacific Journal of Mathematics, 1973 Let Vn(Rn) be the universal ring with respect to em- beddings of the matrix ring Rn into n X n matrix rings over commutative rings. A construction and a representation is given for this ring. As a main tool in the construction, it is proved that every R homomorphism of Rn9 R a com- mutative ring, is the restriction of an inner automorphism of Un, for ...
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Traces on Semigroup Rings and Leavitt Path Algebras [PDF]
, 2015 The trace on matrix rings, along with the augmentation map and Kaplansky trace on group rings, are some of the many examples of linear functions on algebras that vanish on all commutators.
Mesyan, Zachary, Vas, Lia
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Classical quotient rings of generalized matrix rings
International Journal of Mathematics and Mathematical Sciences, 1995 An associative ring R with identity is a generalized matrix ring with idempotent set E if E is a finite set of orthogonal idempotents of R whose sum is 1.
David G. Poole, Patrick N. Stewart
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TRIANGULAR MATRIX REPRESENTATIONS OF SKEW MONOID RINGS [PDF]
, 2010 Let R be a ring and S a u.p.-monoid. Assume that there is a monoid homomorphism α : S → Aut (R). Suppose that α is weakly rigid and lR(Ra) is pure as a left ideal of R for every element a ∈ R.
Xiaoyan, Yang, Zhongkui, Liu
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Sheaves that fail to represent matrix rings [PDF]
, 2014 There are two fundamental obstructions to representing noncommutative rings via sheaves. First, there is no subcanonical coverage on the opposite of the category of rings that includes all covering families in the big Zariski site.
Reyes, Manuel L.
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Proceedings of the American Mathematical Society, 1965 where the ei1 are the usual unit matrices. For example, we could select n left ideals Al, * * *, An of either F or a subring of F and then let Fij=Aj, i, j=1, . I n. If F is a (skew) field and the Fij satisfying (1) are all nonzero, then R defined by (2) is easily shown to be a prime ring.
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Functional identities on upper triangular matrix rings
Open Mathematics, 2020 Let R be a subset of a unital ring Q such that 0 ∈ R. Let us fix an element t ∈ Q. If R is a (t; d)-free subset of Q, then Tn(R) is a (t′; d)-free subset of Tn(Q), where t′ ∈ Tn(Q), tll′$\begin{array}{} t_{ll}' \end{array} $ = t, l = 1, 2, …, n, for any ...
Yuan He, Chen Liangyun
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Transfer matrix simulation of hard-core lattice gases on triangular lattice with up to third-neighbour exclusion [PDF]
Омский научный вестник, 2018 The hard-core lattice gas on a triangular lattice with up to thirdneighbour exclusion has been simulated by the transfer matrix method. To calculate the transfer matrix a special algorithm for generating rings is used.
A. V. Myshlyavtsev, M. D. Myshlyavtseva
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Some Additive Combinatorics Problems in Matrix Rings [PDF]
, 2010 We study the distribution of singular and unimodular matrices in sumsets in matrix rings over finite fields. We apply these results to estimate the largest prime divisor of the determinants in sumsets in matrix rings over the ...
A.N. Skorobogatov +24 more
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