The paper proposes a novel metaheuristic based on integrating chaotic maps into a Henry
gas solubility optimization algorithm (HGSO). The new algorithm is named chaotic Henry …

THE DUAL NOTION OF MULTIPLICATION MODULES Page 1 TAIWANESE JOURNAL OF
MATHEMATICS Vol. 11, No. 4, pp. 1189-1201, September 2007 This paper is available online …

Let R be a commutative ring and M an R-module. In this paper, we study the dual notion of
prime submodules (that is, second submodules of M) and investigate the conditions under …

In this article, we introduce the dual notions of strongly prime, weakly prime, semiprime, and
primal submodules, that is, strongly second, weakly second, semisecond, and secondal …

Let R be an arbitrary ring. A nonzero unital right R-module M is called a second module if M
and all its nonzero homomorphic images have the same annihilator in R. It is proved that if R …

Let R be a commutative ring and M be an R-module. The second spectrum Spec s (M) of M
is the collection of all second submodules of M. We topologize Spec s (M) with Zariski …

Let R be a commutative ring and let M be an R-module. In this paper, we study the dual
notion of prime submodules (that is, second submodules of M). Also we introduce the dual …

In this paper, the notion of fully idempotent modules is defined and it is shown that this
notion inherits most of the essential properties of the usual notion of von Neumann's regular …

Book Journal 2009 V8/1.indb Page 1 CMU. J. Nat. Sci. (2009) Vol. 8(1) S 105 Strong
Comultiplication Modules H. Ansari-Toroghy* and F. Farshadifar Department of Mathematics …

arXiv:1609.08054v1 [math.AC] 26 Sep 2016 Page 1 arXiv:1609.08054v1 [math.AC] 26 Sep
2016 1 SOME GENERALIZATIONS OF SECOND SUBMODULES H. ANSARI-TOROGHY AND …