[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2006.43.4.755

ON THE FLATNESS AND INJECTIVITY OF DUAL MODULES (III)

Huang, Zhaoyong (DEPARTMENT OF MATHEMATICS, NANJING UNIVERSITY)

Publication Information

Bulletin of the Korean Mathematical Society / v.43, no.4, 2006 , pp. 755-762 More about this Journal

Abstract

For a commutative ring R and an injective cogenerator E in the category of R-modules, we characterize von Neumann regular rings and semisimple artinian rings in terms of the properties of dual modules with respect to E.

Keywords

dual modules; quasi-injective; quasi-projective; von Neumann regular rings; semisimple artinian rings;

Citations & Related Records

Times Cited By SCOPUS : 0

Reference

1	F. W. Anderson and K. R. Fuller, Rings and Categories of modules, 2nd ed., Graduate Texts in Mathematics 13, Berlin: Springer-Verlag, 1992
2	T. Albu and C. Nastasescu, Relative Finiteness in Module Theory, Pure and Applied Mathematics (A series of monographs and textbooks) 84, New York: Marcel Dekker, Inc., 1984
3	J. S. Golan, Characterization of rings using quasiprojective modules, Israel J. Math. 8 (1970), 34-38 DOI
4	J. S. Golan, Characterization of rings using quasiprojective modules II, Proc. Amer. Math. Soc. 28 (1971), 337-343
5	P. Griffith, A note on a theorem of Hill, Pacific J. Math. 29 (1969), 279-284 DOI
6	Z. Y. Huang, On the flatness and injectivity of dual modules, Southeast Asian Bull. Math. 21 (1997), no. 3, 257-262
7	T. Ishikawa, Faithfully exact functors and their applications to projective modules and injective modules, Nagoya Math. J. 24 (1964), 29-42 DOI
8	J. J. Rotman, An Introduction to Homological Algebra, New York: Academic Press, 1979
9	B. Stenstrom, Rings of Quotients, Die Grundlehren der Mathematischen Wis-senschaften in Einzeldarstellungen 217, Berlin: Springer-Verlag, 1975
10	Z. Y. Huang and J. Y. Tang, On the flatness and injectivity of dual modules (II), J. Math. Res. Exposition 21 (2001), no. 3, 377-383
11	K. A. Byrd, Some characterizations of uniserial rings, Math. Ann. 186 (1970), 163-170 DOI