The reactions of four-coordinated transition metal macrocyclic complexes [ML](ClO(4))(2) (L = 5,5,7,12,12,14-hexamethyl-1,4,8,11-tetraazacyclotetradecane, M = Ni, Cu) with NH4VO3 under different conditions gave four coordination polymers of {[(CuL)(0.5)(H2L)(1.5)][H2V10O2)] x 6H(2)O}(n) (1x6H(2)O), {[NiL](3)[V16O38(H2O)] x 6H(2)O}(n) (2 x 6H(2)O), {[NiL][VO(3)](2) x 0.33H2O}(n) (3.0.33H(2)O), a...

Let R be a commutative ring with 1 such that Nil(R) is a divided prime ideal of R. The purpose of this paper is to introduce a new class of rings that is closely related to the class of Noetherian rings. A ring R is called a Nonnil-Noetherian ring if every nonnil ideal of R is finitely generated. We show that many of the properties of Noetherian rings are also true for Nonnil-Noetherian rings; ...

Can there be a structure space-type theory for an arbitrary class of ideals ring? The ideal spaces introduced in this paper allows such study and our includes (but not restricted to) prime, maximal, minimal strongly irreducible, completely proper, minimal, primary, nil, nilpotent, regular, radical, principal, finitely generated ideals. We characterise that are sober. introduce the notion discon...

We formulate and prove a geometric version of the Fundamental Theorem of Algebraic K-Theory which relates the K-theory of the Laurent polynomial extension of a ring to the K-theory of the ring. The geometric version relates the higher simple homotopy theory of the product of a nite complex and a circle with that of the complex. By using methods of controlled topology, we also obtain a geometric...

In this work, we focus on reversible cyclic codes which correspond to reversible DNA codes or reversible-complement DNA codes over a family of finite chain rings, in an effort to extend what was done by Yildiz and Siap in [20]. The ring family that we have considered are of size 2 k , k = 1, 2, · · · and we match each ring element with a DNA 2k−1-mer. We use the so-called u-adic digit system to...

The notion of intuitionistic fuzzy sets was introduced by Atanassov as a generalization of the notion of fuzzy sets. In this paper, we consider the notion of intuitionistic nil radicals of intuitionistic fuzzy ideals in commutative rings some properties of such nil radicals. Mathematics Subject Classification: 03E72

Let R be a commutative ring with unity and M unitary module. Nil(M) the set of all nilpotent elements M. The entire element graph over is an undirected E(G(M)) vertex as any two distinct vertices x y are adjacent if only + ∈ Nil(M). In this paper we attempt to study domination in investigate number well bondage its induced subgraphs N(G(M)) Non(G(M)). Some parameters also studied. It has been s...

Throughout this paper, R is an associative ring; andN ,C,C(R), and J denote, respectively, the set of nilpotent elements, the center, the commutator ideal, and the Jacobson radical. An element x of R is called potent if xn = x for some positive integer n= n(x) > 1. A ring R is called periodic if for every x in R, xm = xn for some distinct positive integersm=m(x), n = n(x). A ring R is called we...