notions of strongly regular, regular and left(right) regular $gamma$−semigroupsare introduced. equivalent conditions are obtained through fuzzy notion for a$gamma$−semigroup to be either strongly regular or regular or left regular.

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.

In this article‎, ‎we have characterized ideals in $C(X)$ in which‎ ‎every ideal is also an ideal (a $z$-ideal) of $C(X)$‎. ‎Motivated by‎ ‎this characterization‎, ‎we observe that $C_infty(X)$ is a regular‎ ‎ring if and only if every open locally compact $sigma$-compact‎ ‎subset of $X$ is finite‎. ‎Concerning prime ideals‎, ‎it is shown that‎ ‎the sum of every two prime (semiprime) ideals of e...

‎in this paper‎, ‎we introduce the notion of the radical of a $pmv$-algebra $a$ and we charactrize radical $a$ via elements of $a$‎. ‎also‎, ‎we introduce the notion of the radical of a $cdot$-ideal in $pmv$-algebras‎. ‎several characterizations of this radical is given‎. ‎we define the notion of a semimaximal $cdot$-ideal in a $pmv$-algebra‎. ‎finally we show that $a/i$ has no nilpotent elemen...

It is well-known that the sum of two $z$-ideals in $C(X)$ is either $C(X)$ or a $z$-ideal. The main aim of this paper is to study the sum of strongly $z$-ideals in ${mathcal{R}} L$, the ring of real-valued continuous functions on a frame $L$. For every ideal $I$ in ${mathcal{R}} L$, we introduce the biggest strongly $z$-ideal included in $I$ and the smallest strongly $z$-ideal containing ...

We demonstrate a method to parallelize the computation of a Gröbner basis for a homogenous ideal in a multigraded polynomial ring. Our method uses anti-chains in the lattice N to separate mutually independent S-polynomials for reduction.

There are many patents for magnetic nanoparticles as tumor resonance imaging enhancers, but the gadolinium complexes commonly used in clinic difficult to target diseased tissues, while nanoliposomes ideal carriers anti-tumor drugs.

The notion of vague ideals in pseudo MV-algebras is introduced,and several properties are investigated. Conditions for a vague set to be avague ideal are provided. Conditions for a vague ideal to be implicative aregiven. Characterizations of (implicative, prime) vague ideals are discussed.The smallest vague ideal containing a given vague set is established. Primeand implicative extension proper...