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Commutative equality algebras and &-equality algebras
- Issue Date
- Dec-2020
- Publisher
- Universitaria Publishing House, University of Craiova
- Keywords
- (Commutative) equality algebra; &-equality algebral; o-set; *-set
- Citation
- Annals of the University of Craiova, Mathematics and Computer Science Series, v.47, no.2, pp 331 - 345
- Pages
- 15
- Indexed
- SCOPUS
ESCI
- Journal Title
- Annals of the University of Craiova, Mathematics and Computer Science Series
- Volume
- 47
- Number
- 2
- Start Page
- 331
- End Page
- 345
- ISSN
- 1223-6934
2246-9958
- Abstract
- The notion of &-equality algebras is introduced, and related properties are investigated. Using &-equality algebras, (commutative ordered) semigroups are induced. Conditions for an equality algebra to be an &-equality algebra and commutative equality algebra are provided. The concept of terminal section of an element is introduced, and several properties are studied. Using the notion of terminal section, conditions for an equality algebra to be a commutative equality algebra are considered. Given a subset of an equality algebra, the o-set and the *-set are introduced, and then several related properties are displayed. Conditions for the o-set (resp., *-set) to be deductive systems are stated.
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