Two semigroups are called strongly Morita equivalent if they are contained in a Morita context with unitary bi-acts and surjective
mappings. We consider the notion of context equivalence which is obtained from the notion of strong Morita equivalence by
dropping the requirement of unitariness. We show that context equivalence is an equivalence relation on the class of factorisable
semigroups and describe factorisable semigroups that are context equivalent to monoids or groups, and semigroups with weak
local units that are context equivalent to inverse semigroups, orthodox semigroups or semilattices.
Viêt Trung . Problems and algorithms for affine semigroups . Semigroup Forum , 64 ( 2 ): 180 – 212 , 2002 .  Winfried Bruns and Robert Koch . Normaliz, computing normalizations of affine semigroups .  J. W. S . Cassels . An introduction
In this paper,P-ordered andQ-ordered semigroups are studied. Some characterizations and properties of such semigroups are obtalned. Also the relationship between maximal (minimum) regular ordered semigroups and unitary regular semigroups is investigated.
The purpose of this paper is to describe the structures of the Möbius semigroup induced by the Möbius transformation group
(ℝ, SL(2,ℝ)). In particular, we study stabilizer subsemigoups of Möbius semigroup via the triangle semigroup. In this work,
we obtained a geometric interpretation of the least contraction coefficient function of the Möbius semigroup via the triangle
semigroup and investigated an extension of stabilizer subsemigoups of the Möbius semigroup. Finally, we obtained a factorization
of our stabilizer subsemigoups of the Möbius semigroup.
In this paper we study the congruences of *-regular semigroups, involution semigroups in which every element is p-related
to a projection (an idempotent fixed by the involution). The class of *-regular semigroups was introduced by Drazin in 1979,
as the involutorial counterpart of regular semigroups. In the standard approach to *-regular semigroup congruences, one ,starts
with idempotents, i.e. with traces and kernels in the underlying regular semigroup, builds congruences of that semigroup,
and filters those congruences which preserve the involution. Our approach, however, is more evenhanded with respect to the
fundamental operations of *-regular semigroups. We show that idempotents can be replaced by projections when one passes from
regular to *-regular semigroup congruences. Following the trace-kernel balanced view of Pastijn and Petrich, we prove that
an appropriate equivalence on the set of projections (the *-trace) and the set of all elements equivalent to projections (the
*-kernel) fully suffice to reconstruct an (involution-preserving) congruence of a *-regular semigroup. Also, we obtain some
conclusions about the lattice of congruences of a *-regular semigroup.