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.

We present a set of generators of the full annihilator ideal for the Witt ring of an arbitrary field of characteristic unequal to two satisfying a non-vanishing condition on the powers of the fundamental ideal in the torsion part of the Witt ring. This settles a conjecture of Ongenae and Van Geel. This result could only be proved by first obtaining a new lower bound on the 2-adic valuation of S...

We consider saturation properties of ideals in models obtained by forcing with countable chain condition partial orderings. As sample results, we mention the following. If M[G] is obtained from a model M of GCH via any a-finite chain condition notion of forcing (e.g. add Cohen reals or random reals) then in M[G] every countably complete ideal on <o, is <o3-saturated. If "o-finite chain conditio...

Let (R, m) be a Cohen-Macaulay local ring of dimension d > 0, I an m-primary ideal of R and K an ideal containing I. When depth G(I) ≥ d− 1 and r(I|K) < ∞, we present an upper bound on the second fiber coefficient f2(I, K) of the fiber cones FK(I), and also provide a characterization, in terms of f2(I, K), of the condition depth FK(I) ≥ d− 2.

Is medical research a moral obligation or an option? The relief of suffering is medicine’s noble goal and none would dispute its value. Research is the key to progress in achieving that ideal, the means to that desirable end. Of course, not everything that can be done to achieve that ideal should be done: there are other pressing needs and other ways to improve the human condition. The philosop...

The notions of N-subalgebras and N-closed ideals in BCH-algebras are introduced, and the relation between N-subalgebras and N-closed ideals is considered. Characterizations of Nsubalgebras andN-closed ideals are provided. Using special subsets,N-subalgebras andN-closed ideals are constructed. A condition for anN-subalgebra to be anN-closed ideal is discussed. Given an N-structure, the greatestN...

Almost 20 years ago, W. Narkiewicz posed the problem to give an arithmetical characterization of the ideal class group of an algebraic number field ([13, problem 32]). In the meantime there are various answers to this question if the ideal class group has a special form. (cf. [4], [5], [12] and the literature cited there). The general case was treated by J. Koczorowski [11], F. Halter-Koch [8],...

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.