in this paper, various elementary properties of vague rings are obtained. furthermore, the concepts of vague subring, vague ideal, vague prime ideal and vague maximal ideal are introduced, and the validity of some relevant classical results in these settings are investigated.

(1.2) Let k be an algebraically closed field of arbitrary characteristic. For a ring A, an A-module means a left A-module, unless otherwise specified. However, an ideal of A means a two-sided ideal, not a left ideal. Amod denotes the category of finitely generated A-modules. For a group G, a G-module means a kG-module, where kG is the group algebra of G over k. If V is a finite dimensional vect...

Let R be a nil ring. We prove that primitive ideals in the polynomial ring R[x] in one indeterminate over R are of the form I [x] for some ideals I of R. All considered rings are associative but not necessarily have identities. Köthe’s conjecture states that a ring without nil ideals has no one-sided nil ideals. It is equivalent [4] to the assertion that polynomial rings over nil rings are Jaco...

A generalization of the FGLM technique is given to compute Grr obner bases for two-sided ideals of free nitely generated algebras. Specializations of this algorithm are presented for the cases in which the ideal is determined by either functionals or monoid (group) presentations. Generalizations are discussed in order to compute G-bases on (twisted) semigroup rings. It is well known that the co...

Abs t rac t . "Binary clutters" contain various objects studied in Combinatorial Optimization, such as paths, Chinese Postman Tours, multiflows and one-sided circuits on surfaces. Minimax theorems about these can be generalized in terms of ideal binary clutters. Seymour has conjectured a characterization of these, and the goal of the present work is to study this conjecture in terms of multiflo...

notions of strongly regular, regular and left(right) regular $gamma$−semigroupsare introduced. equivalent conditions are obtained through fuzzy notion for a$gamma$−semigroup to be either strongly regular or regular or left regular.