4 citations · 14 across the 17 of their papers we have counts for
14 papers · 1 filter
The determinant of \(\lll\)-smooth semigroups
M. H. Shahzamanian
This paper continues the investigation of non-zero determinants associated with finite semigroups containing a pair of non-commuting idempotents, as initiated in~\cite{Sha-Det2}. W…
The Layered Catalan Monoids: Structure and Determinants
M. H. Shahzamanian
In this paper, we introduce and study a class of monoids, called Layered Catalan Monoids (\( {LC}_n \)), which satisfy the structural conditions for -smoothness as defined in~…
A step to compute the determinant of finite semigroups not in ECom
M. H. Shahzamanian
The purpose of this paper is to begin studying the computation of the nonzero determinant of semigroups within the class of finite semigroups that possesses a pair of non-commutati…
The determinant of finite semigroups of the pseudovariety ECOM
M. H. Shahzamanian
The purpose of this paper is to compute the non-zero semigroup determinant of the class of finite semigroups in which every two idempotents commute. This class strictly contains th…
Identities of the Jones Monoid
M. H. Shahzamanian
Jones monoids , for , is a family of monoids relevant in knot theory. The purpose of this paper is to characterize of the identities satisfied by the Jones mon…
Nilpotency and strong nilpotency for finite semigroups
J. Almeida, M. Kufleitner, M. H. Shahzamanian
Nilpotent semigroups in the sense of Mal'cev are defined by semigroup identities. Finite nilpotent semigroups constitute a pseudovariety, , which has finite rank. The…
A note on the finite basis and finite rank properties for pseudovarieties of semigroups
J. Almeida, M. H. Shahzamanian
The finite basis property is often connected with the finite rank property, which it entails. Many examples have been produced of finite rank varieties which are not finitely based…
The rank of variants of nilpotent pseudovarieties
J. Almeida, M. H. Shahzamanian
We investigate the rank of pseudovarieties defined by several of the variants of nilpotency conditions for semigroups in the sense of Mal'cev. For several of them, we provide finit…
The pro-nilpotent group topology on a free group
J. Almeida, M. H. Shahzamanian, B. Steinberg
In this paper, we work on the pro-nilpotent group topology of a free group. First we investigate the closure of the product of finitely many subgroups of a free group in the pro-ni…
The congruence on semigroups
M. H. Shahzamanian
In this paper we define a congruence on semigroups. For the finite semigroups , is the smallest congruence relation such that is a nilpotent s…
Finite semigroups that are minimal for not being Malcev nilpotent
E. Jespers, M. H. Shahzamanian
We give a description of finite semigroups that are minimal for not being Malcev nilpotent, i.e. every proper subsemigroup and every proper Rees factor semigroup is Malcev nilp…
Roughness in Cayley Graphs
M. H. Shahzamanian, M. Shirmohammadi, B. Davvaz
In this paper, rough approximations of Cayley graphs are studied and rough edge Cayley graphs are introduced. Furthermore, a new algebraic definition called pseudo-Cayley graphs co…
The Non-Nilpotent Graph of a Semigroup
E. Jespers, M. H. Shahzamanian
We associate a graph with a semigroup (called the upper non-nilpotent graph of ). The vertices of this graph are the elements of and two vertices are…
A description of a class of finite semigroups that are near to being Malcev nilpotent
E. Jespers, M. H. Shahzamanian
In this paper we continue the investigations on the algebraic structure of a finite semigroup that is determined by its associated upper non-nilpotent graph .…