Abstract
This paper obtains a characterisation of the congruences on *-simple type A I-semigroups. The *-locally idempotent-separating congruences, strictly *-locally idempotent-separating congruences and minimum cancellative monoid congruences, are characterised.
Highlights
For a semigroup S, E(S) will denote the set of idempotents of S
The structure theorem for *-simple type A I-semigroups was established in [8], as an extension of the structure theorem for simple I-inverse semigroups and *-simple type A ω-semigroups due to Warne [10] and AsibongIbe [1]
This paper is a follow up of the study of congruences on *-bisimple type A I-semigroups studied by Ndubuisi and Asibong-Ibe [7], where the congruences were identified as idempotent-separating congruence and minimum cancellative monoid congruence
Summary
For a semigroup S, E(S) will denote the set of idempotents of S. Let a be an element of an adequate semigroup S, and a∗ (a†) denotes the unique idempotent in the L∗-class L∗a ( R∗-class Ra∗ ) containing a. Following [9], let T = ⋃di=−01 Mi be a chain of cancellative monoids. Denote a semigroup formed by S = GBR∗(T, θ) where T = ⋃di=−01 Mi. If for each i we let Mi = {ei}, a monoid with one element, we obtain the set I × I under the multiplication (md + i, (n + q − p)d + i)
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