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Generalized F -semigroups

E. Giraldes, P. Marques-Smith, Heinz Mitsch (2005)

Mathematica Bohemica

A semigroup S is called a generalized F -semigroup if there exists a group congruence on S such that the identity class contains a greatest element with respect to the natural partial order ≤ S of S . Using the concept of an anticone, all partially ordered groups which are epimorphic images of a semigroup ( S , · , ≤ S ) are determined. It is shown that a semigroup S is a generalized F -semigroup if and only if S contains an anticone, which is a principal order ideal of ( S , ≤ S ) . Also a characterization by means of the structure...

Generalized inflations and null extensions

Qiang Wang, Shelly L. Wismath (2004)

Discussiones Mathematicae - General Algebra and Applications

An inflation of an algebra is formed by adding a set of new elements to each element in the original or base algebra, with the stipulation that in forming products each new element behaves exactly like the element in the base algebra to which it is attached. Clarke and Monzo have defined the generalized inflation of a semigroup, in which a set of new elements is again added to each base element, but where the new elements are allowed to act like different elements of the base, depending on the context...

Good and very good magnifiers

Marin Gutan (2000)

Bollettino dell'Unione Matematica Italiana

Un elemento a di un semigruppo S è un elemento accrescitivo sinistro se la traslazione λ a di S , associata all'elemento a , è surgettiva e non è iniettiva (E. S. Ljapin, [13], § 5). Così, per ogni elemento accrescitivo sinistro a , esiste un sottoinsieme proprio M di S tale che la restrizione a M di λ a è biunivoca. Se M è un sottosemigruppo (risp. un ideale destro) di S , l'elemento accrescitivo sinistro a viene detto buono (risp. molto buono) (F. Migliorini [15], [16], [17]). Utilizzando il monoide biciclico,...

Green’s 𝒟 -relation for the multiplicative reduct of an idempotent semiring

Francis J. Pastijn, Xian Zhong Zhao (2000)

Archivum Mathematicum

The idempotent semirings for which Green’s 𝒟 -relation on the multiplicative reduct is a congruence relation form a subvariety of the variety of all idempotent semirings. This variety contains the variety consisting of all the idempotent semirings which do not contain a two-element monobisemilattice as a subsemiring. Various characterizations will be given for the idempotent semirings for which the 𝒟 -relation on the multiplicative reduct is the least lattice congruence.

Green's relations and their generalizations on semigroups

Kar-Ping Shum, Lan Du, Yuqi Guo (2010)

Discussiones Mathematicae - General Algebra and Applications

Green's relations and their generalizations on semigroups are useful in studying regular semigroups and their generalizations. In this paper, we first give a brief survey of this topic. We then give some examples to illustrate some special properties of generalized Green's relations which are related to completely regular semigroups and abundant semigroups.

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