We classify all cross-sections of Green’s relations L and R in the Brauer semigroup. The regular behavior of such cross-sections starts from n = 7. We show that in the regular case there are essentially two different cross-sections and all others are Sn-conjugated to one of these two. We also classify all cross-sections up to isomorphism.

The concept of q , -fuzzy ternary subsemigroup (left, right, lateral, quasi-, bi-) ideal of a ternary semigroup is introduced and several related properties are investigated. We give some characterizations of regular and weakly regular ternary semigroups by q , -fuzzy left (right, lateral) ideals, q , -fuzzy quasi-ideals and q , -fuzzy bi-(generalized bi-) ideals.

In this paper we define the concepts of co-medial algebra and regular algebra and we will show that for a regular co-medial algebra (A, f , g), there exist a commutative semigroup (A,+), such that the operations f , g have the linear representation on (A,+). As a consequence of above result, we have the linear representation of an n−ary medial groupoid with an regular element, which was obtaine...

the aim of this paper is to study semigroups possessing $e$-regular elements, where an element $a$ of a semigroup $s$ is {em $e$-regular} if $a$ has an inverse $a^circ$ such that $aa^circ,a^circ a$ lie in $ esubseteq e(s)$. where $s$ possesses `enough' (in a precisely defined way) $e$-regular elements, analogues of green's lemmas and even of green's theorem hold, where green's relations $mbox{$...

We analyze the convex combinations of noninvertible generalized Pauli dynamical maps. By manipulating mixing parameters, one can produce a channel with shifted singularities, additional or even no singularities whatsoever. In particular, we show how to use maps Markovian semigroup. Interestingly, whose results in semigroup are generated by time-local generators and time-homogeneous memory kerne...

We define the notion of weakly ordered semigroups. For this class of semigroups, we compute the radical of the semigroup algebras. This generalizes some results on left regular bands and on 0Hecke algebras.