It is known that the free topological group over the Tychonoff space X, denotedF(X), is aP space if and only ifX is aP -space. This article is concerned with the question of whether one canâ€¦ (More)

A ring is called clean if every element is the sum of a unit and an idempotent. Throughout the last 30 years several characterizations of commutative clean rings have been given. We have compiled aâ€¦ (More)

It is well known that a commutative ring R is complemented (that is, given a âˆˆ R there exists b âˆˆ R such that ab = 0 and a + b is a regular element) if an only if the total ring of quotients of R isâ€¦ (More)

This article maybe used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply orâ€¦ (More)

An element in a ring is called clean if it may be written as a sum of a unit and idempotent. The ring itself is called clean if every element is clean. Recently, Anderson and Camillo (Anderson, D.â€¦ (More)

Let C(X,Z), C(X,Q) and C(X) denote the l-groups of integer-valued, rationalvalued and real-valued continuous functions on a topological space X, respectively. Characterizations are given for theâ€¦ (More)

In the article (Martinez and Zenk, Algebra Universalis, 50, 231â€“257, 2003.), the authors studied several conditions on an algebraic frame L. In particular, four properties called Reg(1), Reg(2),â€¦ (More)

A commutative ring A is said to be clean if every element of A can be written as a sum of a unit and an idempotent. This definition dates back to 1977 where it was introduced by W. K. Nicholson [7].â€¦ (More)