Elementary radical classes

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International Electronic Journal of Algebra
Volume:23 Issue:23
Elementary radical classes

Elementary radical classes

Pages : 25-41

View : 39 | Download : 8

Publication Date : 2018-01-11

Article Type : Research Paper

Abstract :A radical class R of rings is elementary if it contains precisely those rings whose singly generated subrings are in R. Many examples of ele- mentary radical classes are presented, and all those which are either contained in the Jacobson radical class or disjoint from it are described. Attention is given to those elementary radical classes which are de nable by composition subsemigroups of the free ring on one generator. Whether every elementary radical class is of this form remains an open question.
Keywords : Radical class, locally equational, Mal`tsev Neumann product

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