6 papers
Homogeneous Weights on Semigroup Algebras of Finite Commutative Semigroups
M. H. Shahzamanian
The determinant of a finite semigroup is closely related to the Frobenius property of its corresponding semigroup algebra, and it plays a significant role in coding theory applicat…
Simplicity of Augmentation Submodules in Monoids with 0-Minimal Ideals of Rank Greater than Two
M. H. Shahzamanian
In this paper, we construct explicit families of transformation monoids whose augmentation submodules are simple and whose associated 0-minimal J-classes have rank greater than two…
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…
Simplicity of augmentation submodules for transformation monoids
M. H. Shahzamanian, B. Steinberg
For finite permutation groups, simplicity of the augmentation submodule is equivalent to -transitivity over the field of complex numbers. We note that this is not the case for t…