Implicit Linear Differential-Difference Equations in the Module of Formal Generalized Functions over a Commutative Ring

IRRELEVANT ATTACHED PRIME IDEALS OF A CERTAIN ARTINIAN MODULE OVER A COMMUTATIVE RING

Let M be an Artinian module over the commutative ring A (with nonzero identity) and a p spec A be such that a is a finitely generated ideal of A and aM = M. Also suppose that H = H where H. = M/ (0: a )for i

irrelevant attached prime ideals of a certain artinian module over a commutative ring

let m be an artinian module over the commutative ring a (with nonzero identity) and a p spec a be such that a is a finitely generated ideal of a and am = m. also suppose that h = h where h. = m/ (0: a )for i

Linear difference and differential equations

Uniformly Secondary Modules over Commutative Ring

In [2] the notion of “uniformly ideal” was introduced and developed the basic theory. In this article we introduce and advance a theory which, in a sense, dual to that i.e, the notion of “uniformly secondary module”.

Coalgebras Over a Commutative Ring

By a coalgebra over the commutative ring K or a K-coalgebra, we understand a cocommutative, coassociative K-coalgebra with counit. More explicitly we mean a K-module C equipped with maps &C+C&C, subject to the requirement (where we write @ for OK) that the following diagrams commute: CLC@C where the vertical arrow is the one which switches the factors; CAC@C 1 CC38 C@C e@'CtC@C@C, where we have...