Relationships between the canonical ascending and descending central series of ideals of an associative algebra. Issue 5 (4th May 2017)

• Record Type: Journal Article
• Authors: Riley, David; Shahada, Mayada
• Is Part Of: Communications in algebra. Volume 45:Issue 5(2017)
• Page Start: 1969
• Page End: 1982
• Publication Date: 2017-05-04
• Subjects: Central series -- Lie nilpotence -- strong Lie nilpotence -- upper Lie nilpotence -- verbal and marginal subspaces; 16P60 -- 16P70 -- 16R99; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2016.1226871
• Languages: English
• ISSNs: 0092-7872

Abstract

ABSTRACT: We consider the canonical descending and ascending central series of ideals of an associative algebra. In particular, we prove that some ideal in the descending central series is finite-dimensional if and only if some ideal in the ascending central series is finite-codimensional. This result is the associative algebra analogue of results due to Reinhold Baer and Philip Hall in group theory and Ian Stewart in Lie algebra. We also prove various related results.