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Erschienen in:
01.03.2012 | Original Paper
Quotients and weakly algebraic sets in pseudoeffect algebras
Erschienen in: Soft Computing | Ausgabe 3/2012
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Abstract
In the paper, we show that the quotient \([E]_I\) of a lattice-ordered pseudoeffect algebra \(E\) with respect to a normal weak Riesz ideal \(I\) is linearly ordered if and only if \(I\) is a prime normal weak Riesz ideal, and \([E]_I\) is a representable pseudo MV-algebra if and only if \(I\) is an intersection of prime normal weak Riesz ideals. Moreover, we introduce the concept of weakly algebraic sets in pseudoeffect algebras, discuss the characterizations of weakly algebraic sets and show that weakly algebraic sets in pseudoeffect algebra \(E\) are in a one-to-one correspondence with normal weak Riesz ideals in pseudoeffect algebra \(E.\)