This article is cited in 2 papers

Mathematics

T-radicals generated by bimodules

E. A. Timoshenko

Dept. of General Mathematics, Tomsk State University, Tomsk, 634050, Russia

Abstract: We prove that for an arbitrary ring $S$ with identity and an arbitrary left module ${_S}F$ there exists an $S$-$S$-bimodule $N$ such that the conditions $A \otimes_S F = 0$ and $A \otimes_S N = 0$ are equivalent. It is shown that it suffices to set $N = F \otimes S$.

Keywords: module, radical, tensor product, covariant extension, bimodule.

UDC: 512.553+512.541

Received: 07.09.2009
Revised: 07.09.2009