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Weak GE-Morphisms and Qualified GE-Algebras

- Issue Date
- Oct-2023

- Publisher
- SOUTHEAST ASIAN MATHEMATICAL SOC-SEAMS

- Keywords
- GE-algebra; GE-filter; Weak GE-morphism; (Idempotent) Weak GE-endomorphism

- Citation
- SOUTHEAST ASIAN BULLETIN OF MATHEMATICS, v.47, no.5, pp 591 - 609

- Pages
- 19

- Journal Title
- SOUTHEAST ASIAN BULLETIN OF MATHEMATICS

- Volume
- 47

- Number
- 5

- Start Page
- 591

- End Page
- 609

- ISSN
- 0129-2021

0219-175X

- Abstract
- The notions of weak GE-morphism, weak GE-endomorphism are introduced and investigated its properties. Conditions for a self-map on a GE-algebra to be an idempotent and to be a weak GE-endomorphism are provided. The notion of qualified GE-algebra is introduced and its properties are investigated. Condition for a qualified GE-algebra to be an idempotent weak GE-endomorphism is given. The notion of qualified self-map is defined and a necessary and condition for a given self-map on a GE-algebra, the product of two GE-algebras under the qualified self-map to be a qualified GE-algebra is given. For a given qualified GE-algebra, using its kernel, an equivalence relation is induced, and then the quotient set is constructed. A binary operation is given on the quotient set to create a quotient qualified GE-algebra.

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