in this paper, we generalize some results from hilbert c*-modules to pro-c*-algebra case. we also give a new proof of the known result that l2(a) is ahilbert module over a pro-c*-algebra a.

Abstract: Let be a commutative ring and be a unitary module. We define a semiprime submodule of a module and consider various properties of it. Also we define semi-radical of a submodule of a module and give a number of its properties. We define modules which satisfy the semi-radical formula and present the existence of such a module.  

For a polynomial ring, R, in 4n variables over a field, we consider the submodule of R corresponding to the 4 × 4n matrix made up of n groupings of the linear representation of quarternions with variable entries (which corresponds to the Cauchy-Fueter operator in partial differential equations) and let Mn be the corresponding quotient module. We compute many homological properties of Mn includi...

in this paper we introduce the notions of g∗l-module and g∗l-module whichare two proper generalizations of δ-lifting modules. we give some characteriza tions and properties of these modules. we show that a g∗l-module decomposesinto a semisimple submodule m1 and a submodule m2 of m such that every non-zero submodule of m2 contains a non-zero δ-cosingular submodule.

some necessary and sufficient conditions are given for the existence of a g-positive (g-repositive) solution to adjointable operator equations $ax=c,axa^{left( astright) }=c$ and $axb=c$ over hilbert $c^{ast}$-modules, respectively. moreover, the expressions of these general g-positive (g-repositive) solutions are also derived. some of the findings of this paper extend some known results in the...

We show that  higher derivations on a Hilbert$C^{*}-$module associated with the Cauchy functional equation satisfying generalized Hyers--Ulam stability.  

Let M be a Hilbert module of holomorphic functions over a natural function algebra A (Ω), where Ω ⊆Cm is a bounded domain. Let M0 ⊆M be the submodule of functions vanishing to order k on a hypersurface Z ⊆ Ω. We describe a method, which in principle may be used, to construct a set of complete unitary invariants for quotient modules Q = M ⊖M0. The invariants are given explicitly in the particula...

For Y a closed normal subvariety of codimension c of a smooth C–variety X, Brylinski and Kashiwara showed in [BK81] that the local cohomology module HcY (X,OX) contains a unique simple DX– submodule, denoted by L(Y, X). In this paper the analogous result is shown for X and Y defined over a perfect field of finite characteristic. Moreover, a local construction of L(Y,X) is given, relating it to ...

Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. A proper submodule $P$ of $M$ is called strongly prime submodule if $(P + Rx : M)ysubseteq P$ for $x, yin M$, implies that $xin P$ or $yin P$. In this paper, we study more properties of strongly prime submodules. It is shown that a finitely generated $R$-module $M$ is Artinian if and only if $M$ is Noetherian and every st...