Jakubík, J. Basic elements in a pseudo MV-algebra. (English) Zbl 1001.06008 Soft Comput. 5, No. 5, 372-375 (2001). 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. Reviewer: Ivan Chajda (Přerov) Cited in 2 Documents MSC: 06D35 MV-algebras Keywords:\(b\)-atomicity; direct product decomposition; pseudo MV-algebra; basic elements; strong subdirect products PDFBibTeX XMLCite \textit{J. Jakubík}, Soft Comput. 5, No. 5, 372--375 (2001; Zbl 1001.06008) Full Text: DOI