Unit-regularity and representability for semiartinian \(*\)-regular rings. (English) Zbl 07177879

A ring \(R\) is called a \(*\)-ring if \(R\) is endowed with an involution \(r\mapsto r^*\). A \(*\)-ring is called \(*\)-regular if it is (von Neumann) regular and \(rr^* =0\) only for \(r=0\). The main results of the paper show that: (1) Any semiartinian \(*\)-regular ring is unit-regular; (2) If \(R\) is a subdirectly irreducible \(*\)-regular ring with non-zero socle, then it admits a representation within some inner product space.


16E50 von Neumann regular rings and generalizations (associative algebraic aspects)
16W10 Rings with involution; Lie, Jordan and other nonassociative structures
Full Text: DOI arXiv


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