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Published in:
05-01-2021 | Foundations
Locally \(\sigma \)-complete and locally complete EMV-algebras
Published in: Soft Computing | Issue 2/2021
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Abstract
In the paper, we introduce the concept of a locally complete EMV-algebra and a locally \(\sigma \)-complete EMV-algebra. They are generalizations of a complete and \(\sigma \)-complete MV-algebra, respectively. We will find some representations for locally complete EMV-algebras with atomic idempotent elements. We prove that each EMV-algebra of this type is a subdirect product of directly indecomposable complete EMV-algebras with top element. Also, we find a necessary and sufficient condition for a locally complete EMV-algebra when its representing EMV-algebra with the greatest element 1 is complete. Finally, we investigate the Cantor–Bernstein-type theorems for locally \(\sigma \)-complete EMV-algebras and \(\sigma \)-complete EMV-algebras.