Hyper commutative basic algebras, hyper MV-algebras, and states

Jing Wang; Yali Wu; Yichuan Yang

Hyper commutative basic algebras, hyper MV-algebras, and states

Jing Wang
, Yali Wu
, Yichuan Yang^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we introduce hyper commutative basic algebras. We first prove that every hyper MV-algebra is a hyper commutative basic algebra. Then we show that a hyper commutative basic algebra of cardinality 2 is a hyper MV-algebra, which is similar to the result of Botur and Halaš that finite commutative basic algebras coincide with MV-algebras. However, we find a hyper commutative basic algebra of cardinality 3 which is not a hyper MV-algebra. Finally, we study two types of states on hyper commutative basic algebras.

Original language	English
Pages (from-to)	347-364
Number of pages	18
Journal	Journal of Multiple-Valued Logic and Soft Computing
Volume	35
Issue number	3-4
State	Published - 2020

Keywords

Hyper MV-algebras
Hyper commutative basic algebras
Riěcan states
Sup-states

Cite this

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title = "Hyper commutative basic algebras, hyper MV-algebras, and states",

abstract = "In this paper, we introduce hyper commutative basic algebras. We first prove that every hyper MV-algebra is a hyper commutative basic algebra. Then we show that a hyper commutative basic algebra of cardinality 2 is a hyper MV-algebra, which is similar to the result of Botur and Hala{\v s} that finite commutative basic algebras coincide with MV-algebras. However, we find a hyper commutative basic algebra of cardinality 3 which is not a hyper MV-algebra. Finally, we study two types of states on hyper commutative basic algebras.",

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AU - Wu, Yali

AU - Yang, Yichuan

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N2 - In this paper, we introduce hyper commutative basic algebras. We first prove that every hyper MV-algebra is a hyper commutative basic algebra. Then we show that a hyper commutative basic algebra of cardinality 2 is a hyper MV-algebra, which is similar to the result of Botur and Halaš that finite commutative basic algebras coincide with MV-algebras. However, we find a hyper commutative basic algebra of cardinality 3 which is not a hyper MV-algebra. Finally, we study two types of states on hyper commutative basic algebras.

AB - In this paper, we introduce hyper commutative basic algebras. We first prove that every hyper MV-algebra is a hyper commutative basic algebra. Then we show that a hyper commutative basic algebra of cardinality 2 is a hyper MV-algebra, which is similar to the result of Botur and Halaš that finite commutative basic algebras coincide with MV-algebras. However, we find a hyper commutative basic algebra of cardinality 3 which is not a hyper MV-algebra. Finally, we study two types of states on hyper commutative basic algebras.

KW - Hyper MV-algebras

KW - Hyper commutative basic algebras

KW - Riěcan states

KW - Sup-states

UR - https://www.scopus.com/pages/publications/85117383632

M3 - 文章

AN - SCOPUS:85117383632

SN - 1542-3980

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JO - Journal of Multiple-Valued Logic and Soft Computing

JF - Journal of Multiple-Valued Logic and Soft Computing

IS - 3-4

ER -

Hyper commutative basic algebras, hyper MV-algebras, and states

Abstract

Keywords

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