… )) is a von Neumann regular ring. It is proved that M … module is injective. In [14], it was proved
that if every primitive idempotent of a ring R is central (in particular, if R is a commutative ring…

Endomorphism algebras modules with d partially or over commutative rings* … Now we can
apply the same reductions (Propositions 3.3 and 3.8) as in the regular case and we finally …

… case of algebras over a commutative ring. The extension to algebras … regular" which
we shall use later on (§5). For this reason we have introduced the substitute "modular” for “regular…

Let M be an R-module, where R is a commutative ring with identity 1 and let G (V, E) be a
graph. In this paper, we study the graphs associated with modules over commutative rings. We …

… 5,) over a commutative ring R, and it is in fact a kind of prototype: It is nothing but the “odd
analogon” of the polynomial algebra R[x,, . . . . x,] over R. The general super polynomial …

… modules over commutative rings, we start with some definitions in the more general
noncommutative setting. Let R be a ring and M a left R-module… If S consists of regular elements, …

… Hamsher's result for commutative rings has been extended to … Finally we consider when a
strongly n-regular PI-ring is left … 2 to the ring S, we know that S is a strongly n-regular ring. We …

… In this section, we discuss when (MG)RG is a regular module in the sense of Zelmanowitz. …
Therefore, to prove that MG is a regular module over RG, it suffices to show that x(RG)RG is …

… From this we get immediately the equality n = r, proving that R is a regular local ring. As
an application of the preceding Proposition we can give an alternative proof of the Jacobian …