let r be a ring,  be an endomorphism of r and mr be a -rigid module. amodule mr is called quasi-baer if the right annihilator of a principal submodule of r isgenerated by an idempotent. it is shown that an r-module mr is a quasi-baer module if andonly if m[[x]] is a quasi-baer module over the skew power series ring r[[x; ]].

Let Γ be a countable abelian semigroup and A be a countable abelian group satisfying a certain finiteness condition. Suppose that a group G acts on a (Γ × A)-graded Lie superalgebra L = ⊕ (α,a)∈Γ×A L(α,a) by Lie superalgebra automorphisms preserving the (Γ × A)-gradation. In this paper, we show that the Euler-Poincaré principle yields the generalized denominator identity for L and derive a clos...

Following the well-established terminology in commutative algebra, any (not necessarily commutative) finite-dimensional local algebra A $A$ with radical J $J$ will be said to short provided 3 = 0 $J^3 0$ . As case, we show: If a has an indecomposable non-projective Gorenstein-projective module M $M$ , then either is self-injective (so that all modules are Gorenstein-projective) and then, of cou...

Let $(R,fm)$ be a Gorenstein local ring and$M,N$ be two finitely generated modules over $R$. Nagel proved that if $M$ and $N$ are inthe same even liaison class, thenone has $H^i_{fm}(M)cong H^i_{fm}(N)$ for all $iIn this paper, we provide a short proof to this result.

In eukaryotic DNA replication, short RNA-DNA hybrid primers synthesized by primase-DNA polymerase α (Prim-Pol α) are needed to start DNA replication by the replicative DNA polymerases, Pol δ and Pol ϵ. The C terminus of the Pol α catalytic subunit (p180C) in complex with the B subunit (p70) regulates the RNA priming and DNA polymerizing activities of Prim-Pol α. It tethers Pol α and primase, fa...

an r-module m is called strongly noncosingular if it has no nonzero rad-small (cosingular) homomorphic image in the sense of harada. it is proven that (1) an r-module m is strongly noncosingular if and only if m is coatomic and noncosingular; (2) a right perfect ring r is artinian hereditary serial if and only if the class of injective modules coincides with the class of (strongly) noncosingula...

For a cellular algebra A with a cellular basis C, we consider a decomposition of the unit element 1A into orthogonal idempotents (not necessary primitive) satisfying some conditions. By using this decomposition, the cellular basis C can be partitioned into some pieces with good properties. Then by using a certain map α, we give a coarse partition of C whose refinement is the original partition....