AbstractThe following question was posed by Faith in 1964. Suppose that R is a subring of a matrix ring over a division ring with the property that given any non-zero matrix s there exists an element r in R with rs in R and rs ≠ 0. Do there then exist matrix units {eij} and a left order D in their centralizer such that R contains all matrices in ∑jDelj? The purpose of this article is to provide an affirmative answer
In 1953 and 1954, K. Wolfson and D. Zelinsky showed, independently, that every element of the ring o...
AbstractLet D be a division ring and F a subfield of its center. We prove a Wedderburn-Artin type th...
The class of Bézout factorial rings is introduced and characterized. Using the factorial properties...
Matrix rings containing all diagonal matrices, over any coefficient ring R, correspond bijectively t...
AbstractThe following theorem is proved: Let R be a commutative ring. If the ring of all n×n matrice...
This thesis explores the unavoidable substructures of very large matrices with entries over a finite...
AbstractThe set of all 2×2 matrices with elements from a given set Ω is partitioned into a finite nu...
16 pagesLet $n$ and $p$ be non-negative integers with $n \geq p$, and $S$ be a linear subspace of th...
peer reviewedLet the columns of a p×q matrix M over any ring be partitioned into n blocks, M = [M1,....
We prove the following theorem. THEOREM 1. Let SD be any commutative principal ideal ring without di...
AbstractA version of Burnside's theorem states that if F is an arbitrary field and A⊂Mn(F) is an irr...
AbstractLet M be a class of matrices, M∗ a proper subclass of M, and ψ(n) = ψ(n;M,M∗) the largest in...
Abstract. We describe all possible ways how a ring can be expressed as the union of three of its pro...
AbstractTwo square matrices A and B over a ring R are semisimilar, written A⋍B, if YAX=B and XBY=A f...
AbstractSubrings of full matrix rings which have positive row or column rank can be approximated by ...
In 1953 and 1954, K. Wolfson and D. Zelinsky showed, independently, that every element of the ring o...
AbstractLet D be a division ring and F a subfield of its center. We prove a Wedderburn-Artin type th...
The class of Bézout factorial rings is introduced and characterized. Using the factorial properties...
Matrix rings containing all diagonal matrices, over any coefficient ring R, correspond bijectively t...
AbstractThe following theorem is proved: Let R be a commutative ring. If the ring of all n×n matrice...
This thesis explores the unavoidable substructures of very large matrices with entries over a finite...
AbstractThe set of all 2×2 matrices with elements from a given set Ω is partitioned into a finite nu...
16 pagesLet $n$ and $p$ be non-negative integers with $n \geq p$, and $S$ be a linear subspace of th...
peer reviewedLet the columns of a p×q matrix M over any ring be partitioned into n blocks, M = [M1,....
We prove the following theorem. THEOREM 1. Let SD be any commutative principal ideal ring without di...
AbstractA version of Burnside's theorem states that if F is an arbitrary field and A⊂Mn(F) is an irr...
AbstractLet M be a class of matrices, M∗ a proper subclass of M, and ψ(n) = ψ(n;M,M∗) the largest in...
Abstract. We describe all possible ways how a ring can be expressed as the union of three of its pro...
AbstractTwo square matrices A and B over a ring R are semisimilar, written A⋍B, if YAX=B and XBY=A f...
AbstractSubrings of full matrix rings which have positive row or column rank can be approximated by ...
In 1953 and 1954, K. Wolfson and D. Zelinsky showed, independently, that every element of the ring o...
AbstractLet D be a division ring and F a subfield of its center. We prove a Wedderburn-Artin type th...
The class of Bézout factorial rings is introduced and characterized. Using the factorial properties...
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