We characterize those finitely generated commutative rings which are (parametrically) bi-interpretable with arithmetic: a finitely generated commutative ring A is bi-interpretable with (N,+,×) if and only if the space of non-maximal prime ideals of A is nonempty and connected in the Zariski topology and the nilradical of A has a nontrivial annihilator in Z. Notably, by constructing a nontrivial...

Recently Yehuda Rav has given the concept of Semi prime ideals in a general lattice by generalizing the notion of 0-distributive lattices. In this paper we study several properties of these ideals in a general nearlattice and include some of their characterizations. We give some results regarding maximal filters and include a number of Separation properties in a general nearlattice with respect...

This paper deals with polynomial Hermite splines. In the first part, we provide a simple and fast procedure to compute refinement mask of B-splines any order in case general scaling factor. Our is solely derived from reproduction properties satisfied by splines it does not require explicit construction or evaluation basis functions. The second part discusses factorization B-spline masks terms a...

We prove that if a right distributive ring R, which has at least one completely prime ideal contained in the Jacobson radical, satisfies either a.c.c or d.c.c. on principal right annihilators, then the prime radical of R is the right singular ideal of R and is completely prime and nilpotent. These results generalize a theorem by Posner for right chain rings.

Let R be a noncommutative prime ring with its Utumi ring of quotients U , C = Z(U) the extended centroid of R, F a generalized derivation of R and I a nonzero ideal of R. Suppose that there exists 0 = a ∈ R such that a(F ([x, y]) − [x, y]) = 0 for all x, y ∈ I, where n ≥ 2 is a fixed integer. Then one of the following holds: 1. char (R) = 2, R ⊆ M2(C), F (x) = bx for all x ∈ R with a(b − 1) = 0...

We observe that the Poincaré duality isomorphism for a string manifold is an isomorphism of modules over the subalgebra A(2) of the modulo 2 Steenrod algebra. In particular, the pattern of the operations Sq, Sq, and Sq on the cohomology of a string manifold has a symmetry around the middle dimension. We characterize this kind of cohomology operation duality in term of the annihilator of the Tho...