Varieties of Burnside ai-semirings satisfying xn ≈ x

1 June 2021

journal article
research article
Published by Springer Science and Business Media LLC in Acta Scientiarum Mathematicarum

Vol. 87 (1-2), 39-61
https://doi.org/10.14232/actasm-021-164-8

Abstract

We study the ai-semiring variety defined by the identity x(n) approximate to x. We show that some subvarieties of this variety are determined by certain properties of some binary relations and provide equational basis for them. Also, we provide models of the free objects in some subvarieties of this variety.

Keywords

This publication has 18 references indexed in Scilit:

The varieties of semilattice-ordered semigroups satisfying $$x^3\approx x$$ x 3 ≈ x and $$xy\approx yx$$ x y ≈ y x
Periodica Mathematica Hungarica, 2016
On the varieties generated by ai-semirings of order two
Semigroup Forum, 2014
On free Burnside ai-semirings
Semigroup Forum, 2014
On free semilattice-ordered semigroups satisfying x n =x
Semigroup Forum, 2009
Varieties of idempotent semirings with commutative addition
Algebra universalis, 2005
On Varieties of Semilattice-Ordered Semigroups
Semigroup Forum, 2005
Varieties Generated by Ordered Bands II
Order, 2005
Varieties Generated by Ordered Bands I
Order, 2005
$ {\cal L} $-subvarieties of the variety of idempotent semirings
Algebra universalis, 2001
All varieties of regular orthogroups
Semigroup Forum, 1985