[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14403/jcms.2011.24.1.14

MODULE-THEORETIC CHARACTERIZATIONS OF GENERALIZED GCD DOMAINS, II

Kim, Hwankoo (Department of Information Security Hoseo University)

Publication Information

Journal of the Chungcheong Mathematical Society / v.24, no.1, 2011 , pp. 131-135 More about this Journal

Abstract

It is shown that generalized GCD domains satisfy a certain property of injectivity and conversely this property characterizes generalized GCD domains.

Keywords

generalized GCD domain; (quasi-)projective module; ( ${\mathfrak{F}}-$ )injective module;

Citations & Related Records

Reference

1	D. D. Anderson, ${\pi}$ -domains, divisorial ideals, overrings, Glasgow Math. J. 19 (1978), 199-203. DOI
2	D. D. Anderson and D. F. Anderson, Generalized GCD-domains, Comment. Math. Univ. St. Pauli, 23 (1979), 213-221.
3	R. Gilmer, Multiplicative Ideal Theory, Queen's Papers in Pure and Applied Mathematics, vol. 90, Queen's University, Kingston, Ontario, 1992.
4	J. S. Golan, Characterization of rings using quasiprojective modules. II, Proc. Amer. Math. Soc. 28 (1971), 337-343. DOI ScienceOn
5	R. N. Gupta, On f-injective modules and semi-hereditary rings, Proc. Nat. Inst. Sci. India Part A, 35 (1969), 323-328.
6	H. Kim, Module-theoretic characterizations of t-linkative domains, Comm. Algebra 36 (2008), 1649-1670. DOI ScienceOn
7	H. Kim, Module-theoretic characterizations of generalized GCD domains, Comm. Algebra 38 (2010), 759-772. DOI ScienceOn
8	H. Kim, E. S. Kim, and Y. S. Park, Injective modules over strong Mori domains, Houston J. Math. 34 (2008), 349-360.
9	J. J. Rotman, An Introduction to Homological Algebra, 2nd ed., Springer, New York, 2009.
10	F. Wang and R. L. McCasland, On w-modules over strong Mori domains, Comm. Algebra 25 (1997), 1285-1306. DOI ScienceOn