Unit-regularity and representability for semiartinian $*$-regular rings

Christian Herrmann

Address: TUD FB4, Schloßgartenstr. 7, 64289 Darmstadt, Germany

E-mail: herrmann@mathematik.tu-darmstadt.de

Abstract: We show that any semiartinian $*$-regular ring $R$ is unit-regular; if, in addition, $R$ is subdirectly irreducible then it admits a representation within some inner product space.

AMSclassification: primary 16E50; secondary 16W10.

Keywords: *-regular ring, representable, unit-regular.

DOI: 10.5817/AM2020-1-43