真理想为Archimedean子半群的偏序半群

根据真理想情况给出了偏序半群的一种分类，研究了真理想为Archimedean子半群的偏序半群的特征．     

Ring semigroups whose subsemigroups intersect

A multiplicative semigroup S is said to be a ring semigroup provided there exists an addition + on S such that (S,+,⋅) is a ring. In this note, we characterize the ring semigroups S with the property that every two nonzero subsemigroups intersect.     

Ring semigroups whose subsemigroups form a chain

A multiplicative semigroup S is called a ring semigroup if an addition may be defined on S so that (S,+,⋅) is a ring. Such semigroups have been well-studied in the literature (see Bell in Words, Languages and Combinatorics, pp. 24–31, World Scientific, Singapore, 1994; Jones in Semigroup Forum 47(1):1–6, 1993; Jones and Ligh in Semigroup Forum 17(2):163–173, 1979). In this note, we use Mihăilescu’s Theorem (formerly Catalan’s Conjecture) to characterize the ring semigroups whose subsemigroups containing 0 form a chain with respect to set inclusion.     

Commutative semigroups all of whose subsemigroups are densely embedded

Acta Mathematica Hungarica -     

On groups whose all proper subgroups have Chernikov derived subgroups

We study the groups for which the derived subgroups of all proper subgroups are Chernikov subgroups under condition that they possess a normal system whose factors are locally graduated.     

Commutative semigroups whose endomorphisms are power functions

Semigroup Forum - For any commutative semigroup S and positive integer m the power function $$f: S \rightarrow S$$ defined by $$f(x) = x^m$$ is an endomorphism of S. We partly solve the...     

On optimal factorization of free semigroups into free subsemigroups

Optimal factorizations of a subsemigroup into very pure and weakly prefix subsemigroups are considered. It is shown that the intersection of the family of very pure (weakly prefix) subsemigroups containing a given subset A of X⁺ is itself a very pure (weakly prefix) subsemigroup and procedures for constructing the basis of such minimal subsemigroups are provided.