AbstractTwo square matrices A and B over a ring are pseudosimilar if there exist X, Y, and Z satisfying XAY = B, ZBX = A, and XYX = XZX = X. Hartwig and Hall showed this is equivalent to similarity over a field. This result is extended to rings where free modules satisfy a cancellation property. These include rings R with R/rad R artinian (or more generally rings with one in the stable range) and polynomial rings over Dedekind domains. Furthermore, it is shown for commutative rings that if A and B are pseudosimilar, then diag(A, Om) and diag(B, Om) are similar for some m
AbstractCharacterizations are given for elements in an arbitrary ring with involution, having a grou...
We characterize the pseudo-equivalence of a block lower triangular matrix T = [Tij] over a regular r...
AbstractIn this paper static modules and stable Clifford theory are used to obtain a necessary and s...
AbstractTwo square matrices A and B over a ring are pseudosimilar if there exist X, Y, and Z satisfy...
AbstractTwo square matrices A and B over a ring R are semisimilar, written A⋍B, if YAX=B and XBY=A f...
AbstractThe paper studies the problem on matrix similarity over a commutative rings. The conditions ...
AbstractIt is shown that the notion of consimilarity of n-by-n complex matrices is equivalent to eac...
AbstractIt is well known that if A and B are n × m matrices over a ring R, then coker A ≅ coker B do...
AbstractTwo vertices u and v in a graph G are said to be removal-similar if G\u ≅ G\v. Vertices whic...
Let R be a (commutative) local principal ideal ring of length two, for example, the ring R = Z/p(2)Z...
AbstractThis paper discusses the theory of similarity of matrices over a commutative Artinian princi...
AbstractIn this paper, we study the class of rings that satisfy internal direct sum cancellation wit...
AbstractA duality theory for modules over a commutative ring is developed using lattice modules. Usi...
AbstractWasow investigated the problem of when, for a pair of matrices of analytic functions, pointw...
AbstractIt is shown that there is a connection between Roth's theorems on similarity and equivalence...
AbstractCharacterizations are given for elements in an arbitrary ring with involution, having a grou...
We characterize the pseudo-equivalence of a block lower triangular matrix T = [Tij] over a regular r...
AbstractIn this paper static modules and stable Clifford theory are used to obtain a necessary and s...
AbstractTwo square matrices A and B over a ring are pseudosimilar if there exist X, Y, and Z satisfy...
AbstractTwo square matrices A and B over a ring R are semisimilar, written A⋍B, if YAX=B and XBY=A f...
AbstractThe paper studies the problem on matrix similarity over a commutative rings. The conditions ...
AbstractIt is shown that the notion of consimilarity of n-by-n complex matrices is equivalent to eac...
AbstractIt is well known that if A and B are n × m matrices over a ring R, then coker A ≅ coker B do...
AbstractTwo vertices u and v in a graph G are said to be removal-similar if G\u ≅ G\v. Vertices whic...
Let R be a (commutative) local principal ideal ring of length two, for example, the ring R = Z/p(2)Z...
AbstractThis paper discusses the theory of similarity of matrices over a commutative Artinian princi...
AbstractIn this paper, we study the class of rings that satisfy internal direct sum cancellation wit...
AbstractA duality theory for modules over a commutative ring is developed using lattice modules. Usi...
AbstractWasow investigated the problem of when, for a pair of matrices of analytic functions, pointw...
AbstractIt is shown that there is a connection between Roth's theorems on similarity and equivalence...
AbstractCharacterizations are given for elements in an arbitrary ring with involution, having a grou...
We characterize the pseudo-equivalence of a block lower triangular matrix T = [Tij] over a regular r...
AbstractIn this paper static modules and stable Clifford theory are used to obtain a necessary and s...