General bilinear forms

Research output: Contribution to journalArticlepeer-review


We use the generalized correspondence to show that there is a canonical set isomorphism Inn(R) \Aut(R) ≅ Inn(Mn(R))\Aut(Mn(R)), provided RR is the only right R-module N satisfying Nn ≅Rn, and also to prove a variant of a theorem of Osborn. Namely, we classify all semisimple rings with involution admitting no non-trivial idempotents that are invariant under the involution.

We introduce the new notion of general bilinear forms (generalizing sesquilinear forms) and prove that for every ring R (not necessarily commutative, possibly without involution) and every right R-module M which is a generator (i.e., RR is a summand of Mn for some n ∈ ℕ), there is a one-to-one correspondence between the anti-automorphisms of End(M) and the general regular bilinear forms on M, considered up to similarity. This generalizes a well-known similar correspondence in the case R is a field. We also demonstrate that there is no such correspondence for arbitrary R-modules.

Original languageEnglish
Pages (from-to)145-183
Number of pages39
JournalIsrael Journal of Mathematics
Issue number1
StatePublished - Feb 2015
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2015, Hebrew University of Jerusalem.

ASJC Scopus subject areas

  • General Mathematics


Dive into the research topics of 'General bilinear forms'. Together they form a unique fingerprint.

Cite this