A characterization of adequate semigroups by forbidden subsemigroups. http://arxiv.org/abs/1111.4512v1 [math.GR (original) (raw)

A characterization of adequate semigroups by forbidden subsemigroups

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2013

A semigroup is amiable if there is exactly one idempotent in each R * -class and in each L * -class. A semigroup is adequate if it is amiable and if its idempotents commute. We characterize adequate semigroups by showing that they are precisely those amiable semigroups which do not contain isomorphic copies of two particular nonadequate semigroups as subsemigroups.

Semigroups whose idempotents form a subsemigroup

Bulletin of the Australian Mathematical Society, 1990

We prove that if the "type-II-construct" subsemigroup of a finite semigroup S is regular, then the "type-II" subsemigroup of 5 is computable (actually in this case, type-II and type-II-construct are equal). This, together with certain older results about pseudo-varieties of finite semigroups, leads to further results:

Adequate Semigroups

Proceedings of the Edinburgh Mathematical Society, 1979

A monoid in which every principal right ideal is projective is called a right PP monoid. Special classes of such monoids have been investigated in (2), (3), (4) and (8). There is a well-known internal characterisation of right PP monoids using the relation ℒ* which is defined as follows. On a semigroup S, (a,b) ∈ℒ* if and only if the elements a,b of S are related by Green's relation ℒ* in some oversemigroup of S. Then a monoid S is a right PP monoid if and only if each ℒ*-class of S contains an idempotent. The existence of an identity element is not relevant for the internal characterisation and in this paper we study some classes of semigroups whose idempotents commute and in which each ℒ*-class contains an idempotent. We call such a semigroup a right adequate semigroup since it contains a sufficient supply of suitable idempotents. Dually we may define the relation ℛ* on a semigroup and the notion of a left adequate semigroup. A semigroup which is both left and right adequate w...

On a Problem of M. Kambites Regarding Abundant Semigroups

Communications in Algebra, 2012

A semigroup is regular if it contains at least one idempotent in each R-class and in each L-class. A regular semigroup is inverse if satisfies either of the following equivalent conditions: (i) there is a unique idempotent in each R-class and in each L-class, or (ii) the idempotents commute.

On The Properties Shared By a Simple Semigroup with an Identity and Any Semigroup with an Identity

R. H. Bruck's theorem [1] established the fact that any semigroup S can be embedded in a Simple Semigroup which posses an identity element. In this paper, we discuss some of the properties which shares with any semigroup which posses an identity element. Thus we establish the following results i. Any regular (inverse) semigroup can be embedded in a Simple regular (Inverse) semigroup with an identity element ii. There exist simple inverse (and hence, regular) semigroups with an identity element which have an arbitrary cardinal number of D – classes. These results are new extensions arising from [1].

Finite Proper covers in a class of finite semigroups with commuting idempotents

Semigroup Forum, 2003

Weakly left ample semigroups are a class of semigroups that are (2, 1)-subalgebras of semigroups of partial transformations, where the unary operation takes a transformation α to the identity map in the domain of α. It is known that there is a class of proper weakly left ample semigroups whose structure is determined by unipotent monoids acting on semilattices or categories. In this paper we show that for every finite weakly left ample semigroup S , there is a finite proper weakly left ample semigroupŜ and an onto morphism fromŜ to S which separates idempotents. In fact,Ŝ is actually a (2, 1)-subalgebra of a symmetric inverse semigroup, that is, it is a left ample semigroup (formerly, left type A).

Some Classes Of Semigroups That Have Medial Idempotent And Some Construction Theorem

2013

It's known that the set of idempotents of the semigroup, plays an important role forthe structure of this semigroup. Specially, in the regular semigroups, an importantrole plays presence of the medial idempotent and normal medial idempotent.Blyth,T. S and R. B. McFadden have studied and constructed the regular semi groups which contain a normal medial idempotent in terms of idempotent-generated regular semi groups with a normal medial idempotent and inverse semigroups with anidentity. M.Loganathan has described the construction of the regular semigroupswhich contain a medial idempotent. In this paper we will study further properties of medial idempotents on abundant semigroups. We will apply also the constructiontheory of abundant semigroups with a medial idempotent to quasi-adequate semigroups and will make a description of structure of those subsemigroups

On idempotent generated semigroups

Semigroup Forum, 2002

We provide short and direct proofs for some classical theorems proved by Howie, Levi and McFadden concerning idempotent generated semigroups of transformations on a finite set.