Do you want to publish a course? Click here

Unit-regularity and representability for semiartinian *-regular rings

68   0   0.0 ( 0 )
 Added by Christian Herrmann
 Publication date 2019
  fields
and research's language is English




Ask ChatGPT about the research

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.



rate research

Read More

60 - Dayong Liu , Aixiang Fang 2020
Let R be a unit-regular ring, and let a,b,c in R satisfy aba=aca. If ac and ba are group invertible, we prove that ac is similar to ba. Furthermore, if ac and ba are Drazin invertible, then their Drazin inverses are similar. For any ntimes n complex matrices A,B,C with ABA = ACA ,we prove that AC and BA are similar if and only if their k-powers have the same rank. These generalize the known Flanders theorem proved by Hartwig.
79 - Christian Herrmann 2019
Given a subdirectly irreducible *-regular ring R, we show that R is a homomorphic image of a regular *-subring of an ultraproduct of the (simple) eRe, e in the minimal ideal of R; moreover, R (with unit) is directly finite if all eRe are unit-regular. Finally, unit-regularity is shown for every member of the variety generated by artinian *-regular rings (endowed with unit and pseudo-inversion).
296 - Pere Ara 2015
We survey recent progress on the realization problem for von Neumann regular rings, which asks whether every countable conical refinement monoid can be realized as the monoid of isoclasses of finitely generated projective right $R$-modules over a von Neumann regular ring $R$.
We show that a subdirectly irreducible *-regular ring admits a representation within some inner product space provided so does its ortholattice of projections.
143 - Christian Herrmann 2019
We show that a von Neumann regular ring with involution is directly finite provided that it admits a representation as a ring of endomorphisms (the involution given by taking adjoints) of a vector space endowed with a non-degenerate orthosymmetric sesquilinear form.
comments
Fetching comments Fetching comments
Sign in to be able to follow your search criteria
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا