14,099 research outputs found
On the mean value of the Smarandache LCM function
For any positive integer n, the F.Smarandache LCM function SL(n) is defined
as the smallest positive integer k
FP-GR-INJECTIVE MODULES
In this paper, we give some characterizations of FP-grinjective R-modules and graded right R-modules of FP-gr-injective dimension at most n. We study the existence of FP-gr-injective envelopes and FP-gr-injective covers. We also prove that (1) (ā„gr-FI, gr-FI) is a hereditary cotorsion theory if and only if R is a left gr-coherent ring, (2) If R is right gr-coherent with FP-gr-id(RR) ā¤ n, then (gr-FIn, gr-F nā„) is a perfect cotorsion theory, (3) (ā„gr-FIn, gr-FIn) is a cotorsion theory, where gr-FI denotes the class of all FP-gr-injective left R-modules, gr-FIn is the class of all graded right R-modules of FP-gr-injective dimension at most n. Some applications are given
TRIANGULAR MATRIX REPRESENTATIONS OF SKEW MONOID RINGS
Let R be a ring and S a u.p.-monoid. Assume that there is a monoid homomorphism α : S → Aut (R). Suppose that α is weakly rigid and lR(Ra) is pure as a left ideal of R for every element a ∈ R. Then the skew monoid ring R*S induced by α has the same triangulating dimension as R. Furthermore, if R is a PWP ring, then so is R*S.</p
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