Abstract
ABSTRACTThe class of EMV-algebras and the class of lattice generalized effect algebras with RDP which have enough idempotents (EMV-effect algebra for short) are termwise equivalent. We use it to generalize connections between MV-algebras and MV-pairs for the case of EMV-algebras. First, we show that each EMV-algebra M is a homomorphic image of , the generalized Boolean algebra R-generated by M. Then we introduce a concept of an EMV-pair and construct an EMV-algebra using the EMV-pair. We also show that each EMV-algebra can be induced in this way. Then, the concept of an EMV-pair as a generalization of an MV-pair is introduced and some related results are obtained. Finally, we study G-invariant ideals of an EMV-pair .
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