STRUCTURE THEOREMS FOR SOME CLASSES OF GRADE FOUR GORENSTEIN IDEALS

Structure Theory for a Class of Grade Four Gorenstein Ideals

An ideal / in a commutative noetherian ring R is a Gorenstein ideal of grade g if pdR(R/I) = grade I = g and the canonical module HxtsR(R/I, R) is cyclic. Serre showed that if g = 2 then / is a complete intersection, and Buchsbaum and Eisenbud proved a structure theorem for the case g = 3. We present generic resolutions for a class of Gorenstein ideals of grade 4, and we illustrate the structur...

Study and characterization of some classes of polymatroidal ideals

In this paper, the class of polymatroidal ideals are studied. In particular, we show that any polymatroidal ideal has a regular decomposition function, so we can give its explicit resolution. We also characterize generic polymatroidal ideals. Finally, we characterize monomial ideals which all their powers are generalized Cohen-Macaulay polymatroidal ideals.

On some classes of expansions of ideals in $MV$-algebras

In this paper, we introduce the notions of expansion of ideals in $MV$-algebras, $ (tau,sigma)- $primary, $ (tau,sigma)$-obstinate  and $ (tau,sigma)$-Boolean  in $ MV- $algebras. We investigate the relations of them. For example, we show that every $ (tau,sigma)$-obstinate ideal of an $ MV-$ algebra is $ (tau,sigma)$-primary  and $ (tau,sigma)$-Boolean. In particular, we define an expansion $ ...

Some Structure Theorems for

Approximation theorems on some classes of automata

This paper considers a machine as a pair (G5M) where G is a group or a semi group and where M is a state space. The first part of the paper called reversible-state machines considers the case where G is a locally compact group and M is any locally compact group and M is any locally compact space. The essential requirement is that (x,p)~>x(p) be continuous where XGG, peM and x(p)eM; i.e., we req...