the concepts of free modules, projective modules, injective modules and the likeform an important area in module theory. the notion of free fuzzy modules was introducedby muganda as an extension of free modules in the fuzzy context. zahedi and ameriintroduced the concept of projective and injective l-modules. in this paper we give analternate definition for projective l-modules. we prove that e...

The simple 7-dimensional Malcev algebra M is isomorphic to the irreducible sl(2,C)-module V (6) with binary product [x, y] = α(x ∧ y) defined by the sl(2,C)-module morphism α : Λ2V (6)→ V (6). Combining this with the ternary product (x, y, z) = β(x∧y) ·z defined by the sl(2,C)-module morphism β : Λ2V (6)→ V (2) ≈ sl(2,C) gives M the structure of a generalized Lie triple system, or Lie-Yamaguti ...

With the RH1280 and RH1020, Actel Corporation introduces radiation-hardened versions of the popular A1280 and A1020 field programmable gate array (FPGA) familes with equivalent gate densities of 8,000 and 2,000 gate array gates, respectively. These products are processed to the QML process flow as defined in MIL-PRF-38535. They are manufactured with a 0.8 micron, two-level metal epitaxial bulk ...

 Let $R$ be a commutative ring with identity and $M$ be a finitely generated unital $R$-module. In this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. Moreover, we investigate some conditions which imply that the module $M$ is the direct sum of some cyclic modules and free modules. Then some properties of Fitting ideals o...

We introduce a notion of strongly C×-graded, or equivalently, C/Zgraded generalized g-twisted V -module associated to an automorphism g, not necessarily of finite order, of a vertex operator algebra. We also introduce a notion of strongly C-graded generalized g-twisted V -module if V admits an additional C-grading compatible with g. Let V = ∐ n∈Z V(n) be a vertex operator algebra such that V(0)...

$r$-module. in this paper, we explore more properties of $max$-injective modules and we study some conditions under which the maximal spectrum of $m$ is a $max$-spectral space for its zariski topology.

let $r$ be a ring and $m$ a right $r$-module with $s=end_r(m)$. a module $m$ is called semi-projective if for any epimorphism $f:mrightarrow n$, where $n$ is a submodule of $m$, and for any homomorphism $g: mrightarrow n$, there exists $h:mrightarrow m$ such that $fh=g$. in this paper, we study sgq-projective and$pi$-semi-projective modules as two generalizations of semi-projective modules. a m...

let $r$ be a commutative ring with identity and $m$ be a unitary$r$-module. the primary-like spectrum $spec_l(m)$ is thecollection of all primary-like submodules $q$ such that $m/q$ is aprimeful $r$-module. here, $m$ is defined to be rsp if $rad(q)$ isa prime submodule for all $qin spec_l(m)$. this class containsthe family of multiplication modules properly. the purpose of thispaper is to intro...

Enormous potential of cell-based therapeutics is hindered by the lack of effective means to control genetically engineered cells in mammalian tissues. Here, we describe a synthetic module for remote photocontrol of engineered cells that can be adapted for such applications. The module involves photoactivated synthesis of cyclic dimeric GMP (c-di-GMP), a stable small molecule that is not produce...

We study completely positive module maps on $C^{*}$-algebras which are $C^*$-module over another $C^*$-algebra with compatible actions. extend several well known dilation and extension results to this setup, including the Stinespring theorem Wittstock, Arveson, Voiculescu theorems.