Introduction. Let Y be a connected, noncompact Riemann surface, and let A be the ring of all analytic functions on Y. It is known that the ideal theory of the ring A is strikingly similar to the ideal theory of the ring C(X) of all real valued continuous functions on a completely regular topological space X. We show that locally much of the ideal theory of A can be recovered from the ideal theo...

This paper refers to the theory of semirings continuous numerical functions, which has been developed within functional algebra. The object investigation is CP(X) partial functions on topological spaces X with values in field R real numbers. subject study subalgebras CP(X). Some properties lattices A(X) all possible and A1(X) identity are considered. structure atoms preatoms clarified. allowed ...

The set of interval Hausdorff continuous functions constitutes the largest space preserving basic algebraic and topological structural properties of continuous functions, such as linearity, ring structure, Dedekind order completeness, etc. Spaces of interval functions have important applications not only in the construction of numerical methods and algorithms, but to problems in abstract areas ...

In this paper, the concept of pseudoconvexity and quasiconvexity for continuous~-time functions are studied and an equivalence condition for pseudoconvexity is obtained. Moreover, under pseudoconvexity assumptions, some relationships between Minty and Stampacchia vector variational inequalities and continuous-time programming problems are presented. Finally, some characterizations of the soluti...

The lattice of z-ideals of the ring C(X) of real-valued continuous functions on a completely regular Hausdorff space X has been shown by Mart́ınez and Zenk to be a complete Heyting algebra with certain properties. We show that these properties are due only to the fact that C(X) is an f -ring with bounded inversion. This we do by studying lattices of algebraic z-ideals of abstract f -rings with b...

It is well known that a commutative ring R is complemented (that is, given a ∈ R there exists b ∈ R such that ab = 0 and a + b is a regular element) if an only if the total ring of quotients of R is von Neumann regular. We consider generalizations of the notion of a complemented ring and their implications for the total ring of quotients. We then look at the specific case when the ring is a rin...