This paper deals with a question regarding tight closure in characteristic zero which we now review. Let R be a commutative ring of prime characteristic p and let I ⊆ R be an ideal. Recall that for e ≥ 0, the e-th Frobenius power of I, denoted I [p e], is the ideal of R generated by all p-th powers of elements in I. We say that f ∈ I∗, the tight closure of I, if there exists a c not in any mini...

A pseudo-addition in BL-algebras is a binary operation that is associative and non commutative. The aim of this paper is to use the notion of pseudo-addition to study the notion of ideal and fuzzy ideal as a natural generalization of that of ideal and fuzzy ideal in MV-algebras. Using a pseudo-addition, we characterize fuzzy ideals and also obtain a concrete description of the fuzzy ideals gene...

The fundamental concept of a fuzzy set, introduced by Zadeh in his classic paper [5] of 1965, has been applied by many authors to generalize some of the basic notions of algebra. In this note we characterize the semigroups for which each fuzzy ideal is prime, also the semigroups for which each fuzzy right ideal is prime. In Section 2, we prove that a semigroup is fully fuzzy prime if and only i...

Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. Suppose that $phi:S(M)rightarrow S(M)cup lbraceemptysetrbrace$ be a function where $S(M)$ is the set of all submodules of $M$. A proper submodule $N$ of $M$ is called an $(n-1, n)$-$phi$-classical prime submodule, if whenever $r_{1},ldots,r_{n-1}in R$ and $min M$ with $r_{1}ldots r_{n-1}min Nsetminusphi(N)$, then $r_{1...

In this work, we attempt to investigate the connection between various types of ideals (for examples (m,n)-ideal, bi-ideal, interior-ideal, quasi-ideal, prime-ideal and maximal-ideal) of an ordered semigroup (S, ·,≤) and the corresponding, hyperideals of its EL-hyperstructure (S, ∗) (if exists). Moreover, we construct the class of EL-Γ-semihypergroup, associated to a partially-ordered Γsemigroup.

We state several conditions under which comultiplication and weak comultiplication modulesare cyclic and study strong comultiplication modules and comultiplication rings. In particular,we will show that every faithful weak comultiplication module having a maximal submoduleover a reduced ring with a finite indecomposable decomposition is cyclic. Also we show that if M is an strong comultiplicati...

In the p-th cyclotomic field Qpn , p a prime number, n ∈ N, the prime p is totally ramified and the only ideal above p is generated by ωn = ζpn − 1, with the primitive p-th root of unity ζpn = e 2πi pn . Moreover these numbers represent a norm coherent set, i.e. NQpn+1/Qpn(ωn+1) = ωn. It is the aim of this article to establish a similar result for the ray class field Kpn of conductor p over an ...