Let G be a simple, simply connected algebraic group defined and split over the prime field F p > 3. Let F be a finite dimensional rational G-module. As shown in [1] , for d suitably large, the Eilenberg-Mac Lane cohomology groups H*(G(Fpd), V) achieve a stable value H*en(G, V)9 the so-called generic cohomology of V. This generic cohomology can in turn be determined from the rational cohomology ...

Let p denote an odd prime. We show that the spectrum [ E(n), the In-adic completion of Johnson and Wilson’s E(n), admits a unique topological A∞ structure compatible with its canonical ring spectrum structure. Furthermore, the canonical morphism of ring spectra [ E(n) −→ K(n) admits an A∞ structure whichever of the uncountably many A∞ structures of A. Robinson is imposed upon K(n), the n th Mor...

Let G be a group with identity e. R G-graded commutative ring and M graded R-module. We introduce the concept of Ie-prime submodule as generalization prime for I =?g?G Ig fixed ideal R. give number results concerning this class submodules their homogeneous components. A proper N is said to if whenever rg ? h(R) mh h(M) rgmh IeN, then either (N :R M) or N.

Let p be a prime and suppose that K/F is a cyclic extension of degree p with group G. Let J be the FpG-module K/K of pth-power classes. In our previous paper we established precise conditions for J to contain an indecomposable direct summand of dimension not a power of p. At most one such summand exists, and its dimension must be p +1 for some 0 ≤ i < n. We show that for all primes p and all 0 ...

Let G be a semisimple, simply connected algebraic group over an algebraically closed field of prime characteristic p > 0. Let U be the unipotent part of a Borel subgroup B ⊂ G and u the Lie algebra of U . Springer [15] has shown for good primes, that there is a B-equivariant isomorphism U → u, where B acts through conjugation on U and through the adjoint action on u (for G = SLn one has the wel...

Let $R$ be a commutative ring and $M$ be an $R$-module. In this paper, we investigate some properties of 2-absorbing submodules of $M$. It is shown that $N$ is a 2-absorbing submodule of $M$ if and only if whenever $IJLsubseteq N$ for some ideals $I,J$ of R and a submodule $L$ of $M$, then $ILsubseteq N$ or $JLsubseteq N$ or $IJsubseteq N:_RM$. Also, if $N$ is a 2-absorbing submodule of ...

Our aim in this work is to investigate prime submodules and prove some properties of them. We study the relations between a given module extension submodules. The two modules direct product their quotient are studied investigated.

Using a prime number p of memory banks on a vector processor allows a conflict-free access for any slice of p consecutive elements of a vector stored with a stride not multiple of p. To reject the use of a prime number of memory banks, it is generally advanced that address computation for such a memory system would require systematic Euclidean division by the number p. The Chinese Remainder The...

Given a knot K in S 3 and a positive integer p, there is a unique p-fold cyclic connected cover X v --, S 3 K, and this can be completed to a branched cover M e --* S 3. When p is prime, the homology group H1 (M e) is torsion and was one of the earliest knot invariants (predating the Alexander polynomial). It was used by Alexander and Briggs [A-B] to distinguish knots up to 8 crossings and all ...

ANNE E HENKE, UNIVERSIT AT KASSEL Abstra t. Let k be an in nite eld of prime hara teristi and let r be a positive integer. Using admissible de ompositions, we determine expli itly the entries of the de omposition matrix of the S hur algebra S(2; r) over k and prove that any two blo ks with the same number of simple modules have the the same de omposition matrix and hen e the same Cartan matrix...