Commutative Ideals in BE-algebras

“…In 2012, Ahn et al [6] introduced the notion of terminal sections in BE -algebras. In [7], Rezaei and Saeid studied the concept of quotient in commutative BE -algebras. Saeid [8] introduced the notion of Smarandache weak BE -algebra, Q -Smarandache filters and Q -Smarandache ideals.…”

Section: Introductionmentioning

confidence: 99%

A new generalization of BE-algebras

Yiarayong

Wachirawongsakorn

2018

Heliyon

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In this paper we introduce the notion of PSRU-algebras as a generalization of BE-algebras, we investigate its elementary properties. The aim of this paper is to investigate the concept of filters, left ideals (right ideal, ideal) and fuzzy filters in PSRU-algebras. Moreover, we investigate relationships between left ideals and filters in PSRU-algebras. Furthermore, we characterize filters in terms of fuzzy filters. It is shown that if I be a left ideal of a PSRU-algebra X, then Ix is a left ideal of X for all x∈X.

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“…For more details about BCK-algebras, see [14], [30]. Commutative ideals in BCK-algebras were introduced in [29], and they were generalized in [28] and [34] for the case of BCI-algebras and BE-algebras, respectively. This class of ideals proved to play an important role in the study of state BCK-algebras and statemorphism BCK-algebras (see [2]).…”

Section: Introductionmentioning

confidence: 99%

Commutative deductive systems of pseudo-BCK-algebras

Ciungu

2017

Soft Comput

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In this paper we generalize the axiom systems given by M. Pa lasiński, B. Woźniakowska and by W.H. Cornish for commutative BCK-algebras to the case of commutative pseudo BCKalgebras. A characterization of commutative pseudo BCK-algebras is also given. We define the commutative deductive systems of pseudo BCK-algebras and we generalize some results proved by Yisheng Huang for commutative ideals of BCI-algebras to the case of commutative deductive systems of pseudo BCK-algebras. We prove that a pseudo BCK-algebra A is commutative if and only if all the deductive systems of A are commutative. We show that a normal deductive system H of a pseudo BCK-algebra A is commutative if and only if A/H is a commutative pseudo BCK-algebra. We introduce the notions of state operators and statemorphism operators on pseudo BCK-algebras, and we apply these results on commutative deductive systems to investigate the properties of these operators.

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Commutative Ideals in BE-algebras

Cited by 16 publications

References 3 publications

On HvBE-algebras

On HvBE-algebras

A new generalization of BE-algebras

Commutative deductive systems of pseudo-BCK-algebras

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