In this paper, persents the definitions of strongly prime ideal, strongly prime N-subgroup, Pseudo-valuation near ring and Pseudo-valuation N-group. Some of their properties have also been proven by theorems. Then it is shown that, if N be near ring with quotient near-field K and P be a strongly prime ideal of near ring N, then is a strongly prime ideal of ‎‎, for any multiplication subset S of...

D. Buşneag 1 defined pseudo valuation on a Hilbert algebra and proved that every pseudo valuation induces a pseudometric on a Hilbert algebra. Also, D. Buşneag 2 provided several theorems on extensions of pseudo valuations. C. Buşneag 3 introduced the notions of pseudo valuations valuations on residuated lattices, and proved some theorems of extension for these using the model of Hilbert algebr...

Let $X$ be a $BCH$-algebra and $I$ be an ideal of $X$. In this paper, we introduce the concept of $sqrt{I}$. We show that it is an ideal of $X$, when $I$ is closed ideal of $X$. Then we verify some useful properties of it. We prove that it is the ::::union:::: of all $k-$nil ideals of $I$. Moreover, if $I$ is a closed ideal of $X$, then $sqrt{I}$ is a closed translation ideal and so we can cons...

The purpose of this paper is to define the notion of an intervalvalued fuzzy H-ideal(briefly, an i − v fuzzy H-ideal) of a BCI-algebra. Necessary and sufficient conditions for an i − v fuzzy ideal to be an i − v fuzzy H-ideal are stated. A way to make a new i− v fuzzy H-ideal from old one is given. Mathematics Subject Classification: 06F35, 03B52

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...

In this paper some properties of the uniformity topology on a BCI-algebras are discussed. Keywords—(Fuzzy) ideal, (Fuzzy) subalgebra, Uniformity, clopen sets.

As a generalization of neutrosophic set, the notion MBJ-neutrosophic sets is introduced by Mohseni Takallo, Borzooei and Jun, it applied to BCK/BCI-algebras. In this article, set used study commutative ideal in BCI-algebras. The concept closed their properties relationships are studied. conditions for an be given. provided. Characterization established. Finally, extension property founded.