Throughout our discussion, all rings are commutative, Noetherian and have an identity element. The notion of the tight closure of an ideal was developed by M. Hochster and C. Huneke in [HH1] and has yielded many elegant and powerful results in commutative algebra. The theory leads to the notion of F–rational rings, defined by R. Fedder and K.-i. Watanabe as rings in which parameter ideals are t...

Linear codes over finite rings with identity have recently raised a great interest for their new role in algebraic coding theory and for their successful application in combined coding and modulation. Thus, in this paper we address the problems of constructing of new cyclic, BCH, alternant, Goppa and Srivastava codes over local finite commutative rings with identity. These constructions are ver...

Introduction. The main objects of study in this paper are the commutative separable algebras over a commutative ring. Noncommutative separable algebras have been studied in [2]. Commutative separable algebras have been studied in [1] and in [2], [6] where the main ideas are based on the classical Galois theory of fields. This paper depends heavily on these three papers and the reader should con...

During the last 10 years there have been several results on the representation of real polynomials, positive on some semi-algebraic subset of R. These results started with a solution of the moment problem by Schmüdgen for corresponding sets. Later Wörmann realized that the same results could be obtained by the so-called “Kadison-Dubois” Representation Theorem. The aim of our talk is to present ...