R is called commuting regular ring (resp. semigroup) if for each x,y $in$ R there exists a $in$ R such that xy = yxayx. In this paper, we introduce the concept of commuting $pi$-regular rings (resp. semigroups) and study various properties of them.

Owing to the high expressiveness of regular expression, it is frequently used in searching and manipulation of text based data. Regular expression is highly applicable in processing Latin alphabet based text, but the same cannot be said for Hangeul∗, the writing system for Korean language. Although Hangeul possesses alphabetic features within the script, expressiveness of regular expression pat...

Recent developments in additive manufacturing techniques have motivated an increasing number of researchers to study regular porous biomaterials that are based on repeating unit cells. The physical and mechanical properties of such porous biomaterials have therefore received increasing attention during recent years. One of the areas that have revived is analytical study of the mechanical behavi...

We give some characterizations of Lipschitz type spaces slice regular functions in the unit ball skew field quaternions with prescribed modulus continuity.

Let G be a multiplicative group, K a commutative ring with unit, and K(G) the group ring of G with respect to K. We say that K(G) is regular if given an x in K(G), there is a y in K(G) such that xyx = x. Using a homological characterization of regular rings which was found independently by M. Harada [2, Theorem 5] and the author, we prove that if G is locally finite, then K(G) is regular if and...