Abstract In this paper, we investigate some properties of ideals in group algebras finite groups over fields. First, highlight an important link between their dimension, minimal Hamming distance and the order. This is a generalized version uncertainty principle shown 1992 by Meshulam. Secondly, introduce notion Schur product module structure dimension square. We give structural result on that c...

The notion of the sub-exact sequence is generalization exact in algebra especially on a module. A module over ring R vector space field F. Refers to special F when we have complete inner product space, it called Hilbert space. if every Cauchy converges. Now, introduce which can later be useful statistics. This paper aims investigate properties and their relation direct summand As result, get tw...

We study the H n ( 0 ) -module S ? ? due to Tewari and van Willigenburg, which was constructed using new combinatorial objects called standard permuted composition tableaux decomposed into cyclic submodules. First, we show that every direct summand appearing in their decomposition is indecomposable characterize when indecomposable. Second, find characteristic relations among 's expand image of ...

We prove that if $K$ is a nontrivial null-homotopic knot in closed oriented $3$--manfiold $Y$ such $Y-K$ does not have an $S^1\times S^2$ summand, then the zero surgery on summand. This generalizes result of Hom and Lidman, who proved case when irreducible rational homology sphere.

Let A be a commutative noetherian ring of dimension n. Let P be a projective A[T ]-module. Plumstead ([P]) proved that if rankP > dimA then P splits off a free summand of rank one. It is natural to ask what happens when rankP = dimA. In this paper we investigate this question when P has trivial determinant. Let α : P I be a generic surjection (i.e. I ⊂ A[T ] is an ideal of height n). It is prov...

Let X be a normal projective algebraic variety, G its largest connected automorphism group, and A(G) the Albanese variety of G . We determine the isogeny class of A(G) in terms of the geometry of X . In characteristic 0, we show that the dimension of A(G) is the rank of every maximal trivial direct summand of the tangent sheaf of X . Also, we obtain an optimal bound for the dimension of the lar...

Let R be a ring and M a right R-module. It is shown that: (1) M is Artinian if and only if M is a GAS-module and satisfies DCC on generalized supplement submodules and on small submodules; (2) if M satisfies ACC on small submodules, then M is a lifting module if and only if M is a GASmodule and every generalized supplement submodule is a direct summand of M if and only if M satisfies (P ∗); (3)...

We call a finite group Frobenius-like if it has a nontrivial nilpotent normal subgroup F possessing a nontrivial complement H such that ŒF; h D F for all nonidentity elements h 2 H . We prove that any irreducible nontrivial FH -module for a Frobeniuslike group FH of odd order over an algebraically-closed field has an H -regular direct summand if either F is fixed-point free on V or F acts nont...

We generalize the notion of ‘diagonal’ from the class of CSL algebras to masa bimodules. We prove that a reflexive masa bimodule decomposes as a sum of two bimodules, the diagonal and a module generalizing the w*-closure of the Jacobson radical of a CSL algebra. The latter module turns out to be reflexive, a result which is new even for CSL algebras. We show that the projection onto the direct ...