Extensions Papiya Bhattacharjee , Michelle L . Knox , and Warren Wm . McGovern

p - Extensions Papiya Bhattacharjee , Michelle L . Knox , and Warren Wm . McGovern

We consider extensions of unital commutative rings. We define an extension R ↪→ S to be a p-extension if every principally generated ideal of S is generated by an element of R. Examples are plentiful and localizations of regular multiplicative sets are p-extensions. We develop the theory of pextensions.

pg-EXTENSIONS AND p-EXTENSIONS WITH APPLICATIONS TO C(X)

Essential extensions and p-extensions have been studied for commutative rings with identity in various articles, such as [2], [3], and [13]. The present article applies these concepts to certain subrings of C(X). Moreover, the article introduces a new ring extension, called a pg-extension, and determines its relation to both essential extension and p-extension. It turns out that the pg-extensio...

THE CLASSICAL RING OF QUOTIENTS OF Cc(X)

We construct the classical ring of quotients of the algebra of continuous real-valued functions with countable range. Our construction is a slight modification of the construction given in [3]. We supply an example showing that the two constructions can be different.

Feebly Projectable Algebraic Frames and Multiplicative Filters of Ideals

In the article (Martinez and Zenk, Algebra Universalis, 50, 231–257, 2003.), the authors studied several conditions on an algebraic frame L. In particular, four properties called Reg(1), Reg(2), Reg(3), and Reg(4) were considered. There it was shown that Reg(3) is equivalent to the more familiar condition known as projectability. In this article we show that there is a nice property, which we c...

When Min ( A ) - 1 is