Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-13T11:29:32.987Z Has data issue: false hasContentIssue false

Rings in which certain right ideals are direct summands of annihilators

Published online by Cambridge University Press:  09 April 2009

Yiqiang Zhou
Affiliation:
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's A1C 5S7, Canada e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper is a contiunation of the study of the rings for which every principal right ideal (respectively, every right ideal) is a direct summand of a right annihilator initiated by Stanley S. Page and the author in [20, 21].

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Azumaya, G., ‘Finite splitness and finite projectivity’, J. Algebra 106 (1987), 114134.CrossRefGoogle Scholar
[2]Björk, J. E., ‘Rings satisfying certain chain conditions’, J. Reine Angew. Math. 245 (1970), 6373.Google Scholar
[3]Camillo, V., ‘Commutative rings whose principal ideals are annihilators’, Portugal. Math. 46 (1989), 3337.Google Scholar
[4]Camillo, V. and Yousif, M. F., ‘Continuous rings with ACC on annihilators’, Canad. Math. Bull. 34 (1991), 462464.CrossRefGoogle Scholar
[5]Camps, R. and Dicks, W., ‘On semi-local rings’, Israel J. Math. 81 (1993), 203211.CrossRefGoogle Scholar
[6]Chen, J. and Ding, N., ‘On regularity of rings’, Algebra Colloq. 8 (2001) 267274.Google Scholar
[7]Chen, J. and Ding, N., ‘On general principally injective rings’, Comm. Algebra 27 (1999), 20972116.CrossRefGoogle Scholar
[8]Dischinger, F. and Muller, W., ‘Left PF is not right PF’, Comm. Algebra 14 (1986), 12231227.CrossRefGoogle Scholar
[9]Faith, C., ‘Rings with ascending chain conditions on annihilators’, Nagoya Math. J. 27 (1966), 179191.CrossRefGoogle Scholar
[10]Faith, C. and Menal, P., ‘A counter example to a conjecture of Johns’, Proc. Amer. Math. Soc. 116 (1992), 2126.CrossRefGoogle Scholar
[11]Faith, C. and Menal, P., ‘The structure of Johns rings’, Proc. Amer Math. Soc. 120 (1994), 10711081.CrossRefGoogle Scholar
[12]Pardo, J. L. Gómez and GullAsensio, P. A., ‘Torsionless modules and rings with finite essential socle’, in: Abelian groups, module theory, and topology (Padua, 1997) (eds. Dikranjan, D. and Salce, L.), Lecture Notes in Pure and Appl. Math. 201 (Dekker, New York, 1998) pp. 261278.Google Scholar
[13]Goodearl, K. R., Von Neumann regular rings (Pitman, London, 1979).Google Scholar
[14]Johns, B., ‘Annihilatorconditions in noetherian rings’, J. Algebra 30 (1974), 103121.Google Scholar
[15]Nam, S. B., Kim, N. K. and Kim, J. Y., ‘On simple GP-injective modules’, Comm. Algebra 23 (1995), 54375444.CrossRefGoogle Scholar
[16]Nicholson, W. K. and Yousif, M. F., ‘On a theorem of Camillo’, Comm. Algebra 23 (1995), 53095314.CrossRefGoogle Scholar
[17]Nicholson, W. K.Principally injective rings’, J. Algebra 174 (1995), 7793.CrossRefGoogle Scholar
[18]Nicholson, W. K.Mininjective rings’, J. Algebra 187 (1997), 548578.CrossRefGoogle Scholar
[19]Osofsky, B. L., ‘A generalization of quasi-Frobenius rings’, J. Algebra 4 (1966), 373387.CrossRefGoogle Scholar
[20]Page, S. and Zhou, Y., ‘Generalizations of principally injective rings’, J. Algebra 206 (1998), 706721.CrossRefGoogle Scholar
[21]Page, S. and Zhou, Y., ‘Quasi-dual rings’, Comm. Algebra 28 (2000), 489504.CrossRefGoogle Scholar
[22]Puninski, G., Wisbauer, R. and Yousif, M. F., ‘On P-injective rings’, Glasgow Math. J. 37 (1995), 373378.CrossRefGoogle Scholar
[23]Rutter, E. A., ‘Rings with the principal extension property’, Comm. Algebra 3 (1975), 203212.CrossRefGoogle Scholar
[24]Xue, W., ‘A note on YJ-injectivity’, Riv. Mat. Univ. Parma (6) 1 (1998), 3137 (1999).Google Scholar
[25]Yousif, M. F., ‘CS rings and Nakayama permutations’, Com. Algebra 25 (1997), 37873795.CrossRefGoogle Scholar
[26]Yue Chi Ming, R., ‘On injectivity and p-injectivity’, J. Math. Kyoto Univ. 27 (1987), 439452.Google Scholar