The paper uses a new approach to investigate prime submodules and minimal prime submodules of certain modules such as Artinian and torsion modules. In particular, we introduce a concrete formula for the radical of submodules of Artinian modules.

In this paper, for a complete lattice L, we introduce interval-valued L-fuzzy ideal (prime ideal) of a near-ring which is an extended notion of fuzzy ideal (prime ideal) of a near-ring. Some characterization and properties are discussed.

let $g$ be a finite group and let $gk(g)$ be the prime graph of $g$. we assume that $ngeqslant 5 $ is an odd number. in this paper, we show that the simple groups $b_n(3)$ and $c_n(3)$ are 2-recognizable by their prime graphs. as consequences of the result, the characterizability of the groups $b_n(3)$ and $c_n(3)$ by their spectra and by the set of orders of maximal abelian subgroups are obtai...

We use covers of the universal set to de-ne approximation operators on the power set of the given set. In Section 1, we determine basic properties of the upper approximation operator and show how it can be used to give algebraic structural properties of certain subsets. We de-ne a particular cover on the set of ideals of a commutative ring with identity in such a way that both the concepts of t...

In this paper we introduce prime fuzzy ideals over a noncommutative ring. This notion of primeness is equivalent to level cuts being crisp prime ideals. It also generalizes the one provided by Kumbhojkar and Bapat in [16], which lacks this equivalence in a noncommutative setting. Semiprime fuzzy ideals over a noncommutative ring are also defined and characterized as intersection of primes. This...

After the introduction of fuzzy sets by Zadeh [20] in 1965, several researchers have been working on the generalization of the fuzzification. In 1986, Atanassov [2] introduced the notion of intuitionistic fuzzy sets. For more details on the intuitionistic fuzzy sets, we refer to [2-4]. Fuzzy sets are intuitionistic fuzzy sets but the converse is not necessarily true [18]. Kim and Jun [7, 8] int...

In this paper we investgate some properties of fuzzy ideal extension of fuzzy ideal, fuzzy prime ideal, fuzzy semiprime ideal of a Γ−semiring. Among other results we have obtained a characterization of a prime ideal I of a Γ−semiring in terms of fuzzy ideal extension of its characteristic function λI . Mathematics Subject Classification[2000]:16Y60, 16Y99, 03E72

In this paper, we first introduce the new concept of completely semiprime fuzzy ideals of an ordered semigroup S, which is an extension of completely semiprime ideals of ordered semigroup S, and investigate some its related properties. Especially, we characterize an ordered semigroup that is a semilattice of simple ordered semigroups in terms of completely semiprime fuzzy ideals of ordered semi...