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Basic elements in a pseudo MV-algebra. (English) Zbl 1001.06008

The concept of a pseudo MV-algebra was introduced recently by G. Georgescu and A. Iorgulescu, and independently (under the name “generalized MV-algebra”) by J. Rachůnek. An element \(b\) of a pseudo MV-algebra is called basic if \(b\neq 0\) and the interval \([0,b]\) is a chain. The author applies his previous results on direct products of pseudo MV-algebras to the investigation of basic elements. He deals with pseudo MV-algebras where each nonzero element exceeds some basic element. Further, he investigates direct products and strong subdirect products of pseudo MV-algebras.

MSC:

06D35 MV-algebras
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