We study properties determined by idempotents in the following families of matrix
semigroups over a semiring S: the full matrix semigroup M n (S), the semigroup UT n (S) …

We combine matrix theory and graph theory methods to give a complete characterization of
the surjective linear transformations of tropical matrices that preserve the cyclicity index. We …

We study semigroup varieties generated by full and upper triangular tropical matrix
semigroups and the plactic monoid of rank 4. We prove that the upper triangular tropical …

The cyclicity index of a matrix is the cyclicity index of its critical subgraph, namely, the
subgraph of the adjacency graph which consists of all cycles of the maximal average weight …

We study linear functions on the space of n× n matrices over a field which preserve or
strongly preserve each of Green's equivalence relations (L, R, H and J) and the …

We obtain several equivalent characterizations for the Hartwig–Nambooripad order based
on outer inverses. We also introduce new partial orders on arbitrary semigroups extending …

We introduce an equivalence relation ρ on matrices over a class of semirings, which is
relevant to the Kleene star operator on matrices. We characterize those surjective linear …

In this paper we characterize those surjective linear transformations of tropical matrices
preserving the set of all weak transitive closures M n W and the set of all strong transitive …

We study semigroup varieties generated by full and upper triangular tropical matrix
semigroups and the plactic monoid of rank 4. We prove that the upper triangular tropical …

Let R be a commutative local ring whose maximal ideal is generated by a nilpotent element,
and Mat (n, R) be the multiplicative monoid of the square matrices of order n over R. In this …