فهرست مطالب

Algebraic Hyperstructures and Logical Algebras - Volume:1 Issue: 2, 2020
  • Volume:1 Issue: 2, 2020
  • تاریخ انتشار: 1399/03/13
  • تعداد عناوین: 7
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  • Antonio Di Nola *, R. Grigolia, R. Liparteliani Pages 1-7

    One and two-generated free MV -algebras are algebraically described in the variety generated by perfectMV -algebras.

    Keywords: MV -algebra, free algebra, generated free, perfect MV algebra, Variety
  • Young Bae Jun * Pages 9-21

    Two dimensional event set is introduced, and it is applied to algebraic structures. Two dimensional BCK/BCI-eventful algebra, paired B-algebra and paired BCK/BCI-algebra are defined, and several properties are investigated. Conditions for two dimensional eventful algebra to be a B-algebra and a BCK/BCI-algebra are provided. The process of inducing a paired B-algebra using a group is discussed. Using two dimensional BCI-eventful algebra, a commutative group is established.

    Keywords: Two dimensional event (set), two dimensional BCK, BCIeventful algebra, paired Balgebra, paired BCK, BCIalgebra
  • Saber Omidi, Bijan Davvaz *, Jianming Zhan Pages 23-30

    In this paper, we reformulate several results in commutative algebra in terms of commutative hyperrings. We introduce n-hyperideals in commutative hyperrings and give its some basic properties. Based on new definitions and theorems, we obtain some results in the hyperring theory. Also, the paper is stated a characterization for fundamental n-hyperideals.

    Keywords: Commutative hyperring, homomorphism, n-hyperideal
  • Akbar Rezaei, Arsham Borumand Saeid *, Qiuyan Zhan Pages 31-43

    In this paper, we introduce the concept of fuzzy congruence relations on a pseudo BE-algebra and some of properties are investigated. We show that the set of all fuzzy congruence relations is a modular lattice and the quotient structure induced by fuzzy congruence relations is studied.

    Keywords: (pseudo) BE-algebra, (fuzzy) congruence relation, (fuzzy) medial filter
  • Akbar Paad, M. Bakhshi * Pages 45-56

    In this paper, the concept of (strong) hyper equality ideals in bounded hyper equality algebras are introduced and several properties and related results are given. Also, the properties of hyper equality ideals of the direct product of bounded hyper equality algebras are investigated; we prove that any (strong) hyper equality ideal of the direct product of hyper equality algebras is representable with respect to the product of (strong) hyper equality ideals of any direct component. In the sequel, we investigate the relationships between hyper equality ideals and hyper deductive systems in good bounded hyper equality algebras. Furthermore, we show how one can construct a hyper congruence relation via a strong hyper equality ideal so that the congruence classes form a hyper equality algebra.

    Keywords: (Involutive) Hyper equality algebra, (strong) hyper equality ideal, hyper congruence, Direct product
  • Mohammad Mohseni Takallo, Mona Aaly * Pages 57-75

    In this paper, we introduce the notion of MBJneutrosophic sub-algebra and MBJ-neutrosophic filter on equality algebras and investigate some equivalence definitions, properties and the relation between them. Also, by using the notion of MBJ-neutrosophic filter, we introduce a congruence relation on equality algebra and show that the quotient is an equality algebra.

    Keywords: MBJ-neutrosophic set, MBJneutrosophic filter, Equality algebra, Filter
  • Aiyared Iampan *, Akarachai Satirad, Metawee Songsaeng Pages 77-95

    We introduce the concept of UP-hyperalgebras which is a generalization of UP-algebras, and investigate some related properties. Moreover, we introduce the concepts of UP-hypersubalgebras, UP-hyperideals of types 1 and 2, and s-UP-hyperideals of types 1 and 2 in UPhyperalgebras and give some relations among these concepts. We try to show that these concepts are independent by some examples. Furthermore, the closed condition and the R-condition of a nonempty subset are discussed.

    Keywords: UP-hyperalgebra, UP-hyper subalgebra, UP-hyperideal of types 1, 2, s-UPhyperideal of types 1