[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5666/KMJ.2013.53.3.407

t-Prüfer Modules

Kim, Myeong Og (Department of Mathematics, Kyungpook National University)
Kim, Hwankoo (Department of Information Security, Hoseo University)
Oh, Dong Yeol (Division of Liberal Arts, Hanbat National University)

Publication Information

Kyungpook Mathematical Journal / v.53, no.3, 2013 , pp. 407-417 More about this Journal

Abstract

In this article, we characterize t-Pr $\ddot{u}$ fer modules in the class of faithful multiplication modules. As a corollary, we also characterize Krull modules. Several properties of a $t$ -invertible submodule of a faithful multiplication module are given.

Keywords

t-Prufer module; faithful multiplication module; Krull module; t-invertible submodule;

Citations & Related Records

Reference

1	F. H. Al-Alwan and A. G. Naoum, Dedekind modules, Comm. Algebra, 24(1996), 397-421. DOI ScienceOn
2	F. H. Al-Alwan and A. G. Naoum, Dense submodules of multiplication modules, Comm. Algebra, 24(1996), 413-424. DOI ScienceOn
3	M. Ali, Invertiblity of multiplication modules, New Zealand J. Math., 35(2006), 17-29.
4	M. Ali, Some remarks on generalized GCD domains, Comm. Algebra, 36(2008), 142-164. DOI ScienceOn
5	M. Ali, Invertiblity of multiplication modules II, New Zealand J. Math., 39(2009), 45-64.
6	M. Ali and D. J. Smith, Some remarks on multiplication and projective modules, Comm. Algebra, 32(2004), 3897-3909. DOI ScienceOn
7	M. Alkan, B Sarac, and Y. Tiras, Dedekind modules, Comm. Algebra, 33(2005), 1617-1626. DOI ScienceOn
8	M. Alkan and Y. Tiras, Prime modules and submodules, Comm. Algebra, 31(2003), 5253-5261. DOI ScienceOn
9	M. Alkan and Y. Tiras, On Invertible and dense submodules, Comm. Algebra, 32(2004), 3911-3919. DOI ScienceOn
10	Y. Al-Shaniafi and D. D Anderson, Multiplication modules and the ideal ${\theta}(M)$ , Comm. Algebra, 30(2002), 3383-3390. DOI ScienceOn
11	D. D. Anderson, On t-invertibility IV, Factorization in integral domains (Iowa City, IA, 1996), 221-225, Lecture Notes in Pure and Appl. Math., 189, Dekker, New York, 1997.
12	Z. A. El-Bast and P. F. Smith, Multiplication modules, Comm. Algebra, 16(1988), 755-739. DOI
13	V. Erdogdu, Multiplication modules which are distributive, J. Pure Appl. Algebra, 54(1988), 209-213. DOI ScienceOn
14	E. Houston and M. Zafrullah, Integral domains in which each t-ideal is divisorial, Mich. Math. J. 35(1988), 291-300. DOI
15	B. G. Kang, On the converse of a well-known fact about Krull domains, J. Algebra, 124(1989), 284-299. DOI
16	H. Kim and M. O. Kim , Krull modules, Algebra Colloq., 20(2013), 464-474.
17	S. Malik, J. L. Mott, and M. Zafrullah, On t-invertibility, Comm. Algebra, 16(1988), 149-170. DOI
18	J. L. Mott and M. Zafrullah, On Krull domains, Arch. Math., 56(1991), 559-568. DOI
19	P. F. Smith, Some remarks on multiplication modules, Arch. Math., 50(1988), 223-235. DOI ScienceOn
20	M. Zafrullah, Ascending chain condition and star operations, Comm. Algebra, 17(1989), 1523-1533. DOI ScienceOn