We provide an upper bound of the dimension of the maximal projective submodule of the Lie module of the symmetric group of n letters in prime characteristic p, where n = pk with p k.

In the present paper, by considering the notion of MV-modules which is the structure that naturally correspond to lu-modules over lu-rings, we prove some results on prime A-ideals and state some conditions to obtain a prime A-ideal in MV-modules. Also, we state some conditions that an A-ideal is not prime and investigate conditions that $Ksubseteq bigcup _{i=1}^{n}K_{i}$ implies $Ksubseteq K_{j...

A characterization of an h-hemiregular hemiring in terms of a fuzzy h-ideal is provided. Some properties of prime fuzzy h-ideals of h-hemiregular hemirings are investigated. It is proved that a fuzzy subset f of a hemiring S is a prime fuzzy left (right) h-ideal of S if and only if f is two-valued, f(0) = 1, and the set of all x in S such that f(x) = 1 is a prime (left) right h-ideal of S. Fina...

Let $k$ be a totally real number field and $p$ prime. We show that the ``complexity'' of Greenberg's conjecture ($\lambda = \mu 0$) is $p$-adic nature governed (under Leopoldt's conjecture) by finite torsion group ${\mathcal T}_k$ Galois maximal abelian $p$-ramified pro-$p$-extension $k$, means images in ideal norms from layers $k_n$ cyclotomic tower (Theorem (5.2)). These are obtained via form...

An rj-normal lattice is a distributive lattice with 0 such that each prime ideal contains at most n minimal prime ideals. A relatively ra-normal lattice is a distributive lattice such that each bounded closed interval is an /¡.-normal lattice. The main results of this paper are: (1) a distributive lattice L with 0 is 71,-normal if and only if for any %n, x,,*•', X e L such that x Ax. = 0 for an...

We study the charmless two-body decays of $B\to {\bf B}_n \overline{\bf B}_n^\prime$ with $B = ( B^+ , B^0 B^0_s)$ and ${\bf B}_n^{(\prime)}$ low-lying octet baryons. The factorizable amplitudes are calculated by modified bag model, while nonfactorizable ones extracted from experimental data $SU(3)_F$ flavor symmetry. able to explain all current measurements provide predictions on decay branchi...

Let p be a prime number and F an algebraic closure of the finite field Fp with p elements. Let n and N denote positive integers, N prime to p. We are interested in representations of the Galois group GQ = Gal(Q̄/Q) into GL(n,F), unramified at all finite primes not dividing pN . (We shall say “ρ is unramified outside pN .”) In this paper, “representation” will always mean “continuous, semisimple ...

we generalize concepts of left hyperfilters, right hyperfilters and an ordered semihypergroup by introducing left-m-hyperfilters, right-n-hyperfilters (m,n)-hyperfilters semihypergroup. Then, some properties these generalized have been studied. Finally, left-m-hyperfilters (resp. right-n-hyperfilters, (m,n)-hyperfilters) (m, 0)-regular (0,n)-regular, (m,n)-regular) semihypergroups characterize in terms...

Alon, Babai and Suzuki proved the following theorem: Let p be a prime and let K , L be two disjoint subsets of {0, 1, . . . , p − 1}. Let |K | = r, |L| = s, and assume r(s − r + 1) ≤ p − 1 and n ≥ s + kr where kr is the maximal element of K . Let F be a family of subsets of an n-element set. Suppose that (i) |F | ∈ K (mod p) for each F ∈ F; (ii) |E ∩ F | ∈ L (mod p) for each pair of distinct se...