… Conversely, given any scalar b ∈ F, we get a one-dimensional simple g-module,
denoted by Mb, in which h acts as multiplication by b, and g′ acts trivially. Case 2 a = 0. …

… Throughout this paper, we define q as a given power of a prime p > 2, Fq the finite field of q
elements and k the algebraic closure Fq of Fq. All the vector spaces and modules are of finite …

In this paper, we studied representations of finite-dimensional Lie superalgebras over an
algebraically closed field $\mathbb {F} $ of characteristic p> 2. It was shown that simple …

… the modified induced modules of graded Lie algebras of Cartan types W, S, H coincide with
coinduced modules. The relationship between induced modules and coinduced modules …

… Corolary2 Let Pbe a propersubmodule ofa finitely generated faithful multiplication R-module
M,then Pis almost primary in Mifand only if whenevern,me Msuch thatnm EP一(P:Af)P, …

… The main work of James and Dipper is to create a full list of irreducible representations of
GLn in the module phase, both ordinary and p-modular, with the natural label (σ, λ) we defined …

… If M is a right R-module then the Krull dimension of M, written K(M), is defined to be the
deviation of L(M), the lattice of submodules of M. In … Then we multiply the monomials and get …

… Every GK-module (resp. Gv-module) A considered in this thesis is a continuous module in
the sense that the stabilizer of every element of A is an open subgroup of GK (resp. Gv). Let Hq…

… If M is both a left A-module and a left L-module, then we claim that M is a left A♯L-module …
Next we will prove that f is both a left A-module map and a left L-module map. As a …

A theorem of F. Hirzebruch relates continued fractions to class numbers of quadratic number
fields. A version for function fields of odd characteristic was established by DR Hayes and …