The rank of a commutative cancellative semigroup S is the cardinality of a maximal independent subset of S. Commutative cancellative semigroups of finite rank are subarchimedean and thus admit a Tamura-like representation. We characterize these semigroups in several ways and provide structure theorems in terms of a construction akin to the one devised by T. Tamura for N-semigroups.

This is a survey on recent developments of the theory of one-parameter semigroups and evolution equations with special emphasis on functional calculus and kernel estimates. Also other topics as asymptotic behavior for large time and holomorphic semigroups are discussed. As main application we consider elliptic operators with various boundary conditions. Semigroups and evolution equations: Funct...

We consider certain abundant semigroups in which the idempotents form a subsemigroup, and which we call bountiful semigroups. We find a simple criterion for a finite bountiful semigroup to be a member of the join of the pseudovarieties of finite groups and finite aperiodic semigroups.

1. J. F. Berglund and K. H. Hofmann, Compact semitopological semigroups and weakly almost periodic functions, Lecture Notes in Math., vol. 42, Springer-Verlag, Berlin and New York, 1967. MR 36 #6531. 2. Mary Katherine Bennett, Review of "Distributive Lattices by R. Balbes and P. Dwinger," Bull. Amer. Math. Soc. 82 (1976), 246-249. 3. R. Burckel, Weakly almost periodic functions on semigroups, G...

In this paper, the study of vague structures of Γ-semigroups is initiated by introducing the concepts of vague subsemigroup, vague bi-ideal and vague (1, 2)-ideal in a Γ-semigroup and some fundamental results are obtained. Then the concept of vague weakly completely prime ideals in Γ-semigroups has been introduced and studied directly and via operator semigroups

Xiaomin Zhang Department of Mathematics, Linyi Normal University, Shandong 276005, China E-mail: [email protected] Abatract The aim of this paper is to study eventually strong wrpp semigroups whose idempotents satisfy permutation identities, that is, so-called PI-strong wrpp semigroups. After some properties are obtained, the structure of such semigroups are investigated. In particular, the struct...

In this paper we have studied   q   , -fuzzy semiprime ideals in semigroups. We have characterized completely regular semigroups by the properties of their   q   , -fuzzy quasi ideals. Moreover we have characterized semigroups that are semilattices of groups by   q   , -fuzzy quasi ideals.

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.

The action of any group on itself by conjugation and the corresponding conjugacy relation play an important role in group theory. There have been several attempts to extend the notion of conjugacy to semigroups. In this paper, we present a new definition of conjugacy that can be applied to an arbitrary semigroup and it does not reduce to the universal relation in semigroups with a zero. We comp...