Journal of Algebraic Hyperstructures and Logical Algebras
http://jahla.hatef.ac.ir/
Journal of Algebraic Hyperstructures and Logical Algebrasendaily1Tue, 01 Nov 2022 00:00:00 +0330Tue, 01 Nov 2022 00:00:00 +0330Near Krasner hyperrings on nearness approximation space
http://jahla.hatef.ac.ir/article_163690.html
Krasner hyperrings are a generalization of rings. Indeed, in a Krasner hyperring the addition is a hyperoperation, while the multiplication is an ordinary operation. On the other hand, a generalization of rough set theory is the near set theory. Now, in this paper we are interested in combining these concepts. We study and investigate the notion of near Krasner&nbsp; hyperrings on a nearness approximation space. Also, we define near subhyperring, near hyperideal, near homomorphism&nbsp; and prove some results and present several examples in this respect.Relations between L-algebras and other logical algebras
http://jahla.hatef.ac.ir/article_166948.html
In this paper, by considering the notion of L-algebra, &nbsp;we show that there are relations between L-algebras and some of other logical algebras such as residuated lattices, MTL-algebras, BL-algebras, MV-algebras, BCK-algebras, equality algebras, EQ-algebras and Hilbert algebras. The &nbsp;aim of this paper is to find &nbsp;under what conditions L-algebras are equivalent to these logical algebras.Commutative ideals of BCI-algebras based on Łukasiewicz fuzzy sets
http://jahla.hatef.ac.ir/article_154328.html
With the aim of applying the Łukasiewicz fuzzy set to commutative ideal in BCI-algebras, the concept of Łukasiewicz fuzzy commutative ideal is introduced, and its properties are investigated. The relationship between a Łukasiewicz fuzzy ideal and a Łukasiewicz fuzzy commutative ideal are discussed. After providing an example of a Łukasiewicz fuzzy ideal, not a Łukasiewicz fuzzy commutative ideal, conditions under which a Łukasiewicz fuzzy ideal can be a Łukasiewicz fuzzy commutative ideal are explored. Characterizations of Łukasiewicz fuzzy commutative ideals are displayed. Conditions under which $\in$-set, q-set, and O-set can be commutative ideals are found.&nbsp;On ringoids
http://jahla.hatef.ac.ir/article_160777.html
In this paper, we introduce the notion of a ringoid, and we obtain left distributive ringoids over a field which are not rings. We introduce several different types of ringoids, and also we discuss on (r, s)-ringoids. Moreover, we discuss geometric observations of the parallelism of vectors in several ringoids.&nbsp;Primary decomposition of A-ideals in MV-semimodules
http://jahla.hatef.ac.ir/article_158947.html
In [16], by using an MV-semiring and an MV-algebra, we introduced the new definition&nbsp; of MV-semimodule and studied some of their basic properties. In this paper, we study&nbsp; and present definitions of primary ideals of MV-semirings, decomposition of ideals in&nbsp; MV-semirings, primary A-ideals of MV -semimodules, and decomposition of A-ideals in MV-semimodules. Then we present some conditions that an A-ideal can have a reduced primary decomposition.&nbsp;On the equivalence of sequences dependent on fuzzy ideals in the BCI-algebra
http://jahla.hatef.ac.ir/article_161670.html
Murali and Makamba (2001) introduced an equivalence of fuzzy subgroups. Dudek and Jun (2004) studied the equivalence defined by Murali and Makamba in fuzzy ideals of a BCI-algebra. In this paper, we obtained a sequence of fuzzy ideals of a BCI-algebra X from a fuzzy ideal on X. We will show that, if two fuzzy ideals are equivalent, then the sequence of fuzzy ideals obtained from them are equivalent. We show that there is a relationship between a fuzzy ideal with BCI-algebra X and a fuzzy ideal with adjoint BCI-algebra A, where A is an Abelian subgroup of Aut&micro;(X).n-fold 2-nilpotent(solvable) ideal of a BCK-algebra
http://jahla.hatef.ac.ir/article_164773.html
In this paper, &nbsp;first &nbsp;we introduce the notions of k-nilpotent (solvable) ideals &nbsp;and k-nilpotent BCK-algebras. Specially, we show &nbsp;that every commutative ideal is 1-nilpotent (solvable). Second, we state &nbsp;an equivalent condition to k-nilpotency (solvablity) ideals and &nbsp;BCK-algebra. Finally, &nbsp;we study n-fold 2-nilpotent (solvable) ideals and BCK-algebras as a generalization of n-fold commutative ideals and BCK-algebras, and we study the relation between these two concepts. Basically, we compare 2-nilpotent and solvable ideals (BCK-algebras).