[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2005.42.3.527

COUNTABLE RINGS WITH ACC ON ANNIHILATORS

HIRANO YASUYUKI (DEPARTMENT OF MATHMATHICS, OKYAMA UNIVERSITY)
KIM HONG KEE (DEPARTMENT OF MATHMATHICS, GYEONGSANG NATIONAL UNIVERSITY)

Publication Information

Bulletin of the Korean Mathematical Society / v.42, no.3, 2005 , pp. 527-534 More about this Journal

Abstract

We consider countable rings with ascending chain condition on right annihilators. We determine the structure of a countable right p-injective Baer ring, a countable semi prime quasi-Baer ring and a countable quasi-Baer biregular ring.

Keywords

countable ring; ascending chain condition on annihilators;

Citations & Related Records

Reference

1	E. P. Armendariz, On semiprime rings of bounded index, Proc. Amer. Math. Soc. 85 (1982), 146-148
2	G. F. Birkenmeier, J. Y. Kim and J. K. Park, Rings with countably many direct summands, Comm. Algebra 28 (2000), 757-769 DOI ScienceOn
3	C. Faith, Rings with ascending condition on annihilators, Nagoya Math. J. 27 (1966), 179-191 DOI
4	E. Formanek, Noetherian PI-rings, Comm. Algebra 1 (1974), 79-86 DOI ScienceOn
5	J. Hannah, Quotient rings of semiprime rings with bounded index, Glasg. Math. J. 23 (1982), 53-64 DOI
6	Y. Hirano, On nonsingular p-injective rings, Publ. Mat. 38 (1994), 455-461 DOI
7	N. Jacobson, Structure of Rings, Amer. Math. Soc. Colloq. Publ. 37, Providence, R. I., 1964
8	J. Y. Kim and J. K, Park, When is a regular ring a semisimple Artinian ring?, Math. Japonica 45 (1997), 311-313
9	B. Stenstrom, Rings of Quotients, Springer-Verlag, Berlin-Heidelberg-New York, 1975
10	M. Ikeda and T. Nakayama,, On some characteristic properties of quasi-Frobenius and regular rings, Proc. Amer. Math. Soc. 5 (1954), 15-18
11	C. Lanski, The cardinality of the center of a PI-ring, Canad. Math. Bull. 41 (1998), 81-85 DOI
12	K. M. Rangaswamy, Regular and Baer rings, Proc. Amer. Math. Soc. 42 (1974), 354-358