Numerous studies indicate that evolutionary concepts can and should be taught at the primary school level. However, teaching evolution in is presumably not yet norm globally. At same time, educational potential of lies their applicability to many curriculum topics natural social sciences. Capitalizing on this requires broad teacher content knowledge (CK) pedagogical (PCK) about concepts. much k...

let r be a ring, m a right r-module and (s,≤) a strictly ordered monoid. in this paper we will show that if (s,≤) is a strictly ordered monoid satisfying the condition that 0 ≤ s for all s ∈ s, then the module [[ms,≤]] of generalized power series is a uniserial right [[rs,≤]] ]]-module if and only if m is a simple right r-module and s is a chain monoid.

Let $A$ be a Banach algebra and $E$ be a Banach $A$-bimodule then $S = A oplus E$, the $l^1$-direct sum of $A$ and $E$ becomes a module extension Banach algebra when equipped with the algebras product $(a,x).(a^prime,x^prime)= (aa^prime, a.x^prime+ x.a^prime)$. In this paper, we investigate $triangle$-amenability for these Banach algebras and we show that for discrete inverse semigroup $S$ with...

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...

 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...

Let M be a graded leftA-module and M∗ the associate complex of M. Then : If is noetherian (resp. artinian) then strongly hopfian cohopfian); cohopfian), leftA-module, M, N submodule N∗ fully invariant subcomplex M∗. M∗/N∗ hopfian, hopfian. if all cohopfian, cohopfian.

$r$-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...

<p>Let R be a commutative ring with identity and M unitary R-module. The primary-like spectrum Spec<sub>L</sub>(M) is the collection of all submodules Q M, recent generalization primary ideals, such that M/Q primeful In this article, we topologies patch-like topology, show when, topology quasi-compact, Hausdorff, totally disconnected space.</p>

The paper describes an approach to developing an interactive MT system for translating technical texts on the example of translating patent claims between Russian and English. The approach conforms to the human-aided machine translation paradigm. The system is meant for a source language (SL) speaker who does not know the target language (TL). It consists of i) an analysis module which includes...