We prove an explicit log-free zero density estimate and an explicit version of the zero-repulsion phenomenon of Deuring and Heilbronn for Hecke L-functions. In forthcoming work of the second author, these estimates will be used to establish explicit bounds on the least norm of a prime ideal in a congruence class group and improve upon existing explicit bounds for the least norm of a prime ideal...

Let R be a commutative ring with identity and M an R–module. If M is either locally cyclic projective or faithful multiplication then M is locally either zero or isomorphic to R. We investigate locally cyclic projective modules and the properties they have in common with faithful multiplication modules. Our main tool is the trace ideal. We see that the module structure of a locally cyclic proje...

A characteristic set theory for partial difference polynomial systems is proposed. We introduce the concept of coherent and regular ascending chains and prove that a partial difference ascending chain is the characteristic set of its saturation ideal if and only if it is coherent and regular. This gives a method to decide whether a polynomial belongs to the saturation ideal of an ascending chai...

Recently, it was shown that a binary linear code can be associated to a binomial ideal given as the sum of a toric ideal and a non-prime ideal. Since then two different generalizations have been provided which coincide for the binary case. In this paper, we establish some connections between the two approaches. In particular, we show that the corresponding code ideals are related by elimination...

We propose a technique for obtaining solutions to ordinary differential equations. A system of differential equations sometimes has multiple solutions with distinct features. Prime ideal decomposition can be used for extracting the desired solution from these solutions. Solutions to algebraic equations contain many parameters, and in such a case, prime ideal decomposition is less tractable. As ...

In this paper we shall introduce the concept of prime and semiprime bi-ideals of ordered semigroups and we give characterizations of prime bi-ideal and regular of ordered semigroups. Mathematics Subject Classification: 06F05

We characterize d-lattices as those bounded lattices in which every maximal filter/ideal is prime, and we show that a d-lattice is complemented iff it is balanced iff all prime filters/ideals are maximal.

In this paper, T. K. Dutta`s and S. K. Sardar`s semiprime ideal of -rings as a fuzzy semiprime ideal of a -rings via its operator rings was defined. Some characterizations of fuzzy semiprime ideal of -rings was obtained. That is; a characterization prove of a fuzzy semiprime ideal, the relationship between fuzzy semiprime ideal and fuzzy prime ideal was obtained. If is fuzzy semiprime ideal of ...

In this paper, we introduce the notions of interval-valued fuzzy prime (resp. strongly prime and semiprime) bi-ideals of a semigroup. By using these ideas we characterize those semigroups for which each interval-valued fuzzy bi-ideal is semiprime and strongly prime.

The Ritt problem asks if there is an algorithm that tells whether one prime differential ideal is contained in another one if both are given by their characteristic sets. We give several equivalent formulations of this problem. In particular, we show that it is equivalent to testing if a differential polynomial is a zero divisor modulo a radical differential ideal. The technique used in the pro...