No abstract

The aim of this paper is to determine several saturated classes of structurally regular semigroups. First, we show that structurally (n,m)-regular semigroups are saturated in a subclass of semigroups for any pair (n,m) of positive integers. We also demonstrate that, for all positive integers n and k with 1≤k≤n, the variety of structurally (0,n)-left seminormal bands is saturated in the variety of structurally (0,k)-bands. As a result, in the category of structurally (0,k)-bands, epis from structurally (0,n)-left seminormal bands is onto.

We show that for each $$n\ge 2\in {\mathbb {N}}$$ n ≥ 2 ∈ N , the varieties $${\mathbb {V}}_{n}=[x_1x_2x_3=x_1^nx_{i_1}x_{i_2}x_{i_3}]$$ V n = [ x 1 x 2 x 3 = x 1 n x i 1 x i 2 x i 3 ] where i is any non-trivial permutation of $$\{1,2,3\}$$ { 1 , 2 , 3 } are closed. Further, we show that for each $$n\in {\mathbb {N}}$$ n ∈ N , the varieties $${\mathcal {V}}_{n}=[x_1x_2x_3=x_1^nx_{i_1}x_{i_2}x_{i_3}]$$ V n = [ x 1 x 2 x 3 = x 1 n x i 1 x i 2 x i 3 ] where i is any non-trivial permutation of $$\{1,2,3\}$$ { 1 , 2 , 3 } other than the permutation (231) are closed.

In this paper, we find sufficient conditions for some commutative varieties of semigroups to be closed under dominions.

In this paper, we first show that the variety [Formula: see text] of posemigroups satisfying an identity [Formula: see text] is closed if it is [Formula: see text]-convex. Next, we show that inverse posemigroups satisfying an identity [Formula: see text] are absolutely closed. We also show that a convex variety of left [right] zero posemigroups is absolutely closed and finally [Formula: see text] is absolutely closed if so is [Formula: see text].