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On p-injective rings

Published online by Cambridge University Press:  18 May 2009

Gennadi Puninski ,
Robert Wisbauer  and
Mohamed Yousif
Gennadi Puninski
Affiliation:
Russian Social Institute, Losionostrovskaja, 24 107150 Moscow, Russia
Robert Wisbauer
Affiliation:
Mathematisches Institut der Universität, Universitätsstr. 1, 40225 Düsseldorf, Germany
Mohamed Yousif
Affiliation:
Department of Mathematics, Ohio State University, Lima, Ohio 45804, USA
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Throughout this paper R will be an associative ring with unity and all R-modules are unitary. The right (resp. left) annihilator in R of a subset X of a module is denoted by r(X)(resp. I(X)). The Jacobson radical of R is denoted by J(R), the singular ideals are denoted by Z(RR) and Z(RR) and the socles by Soc(RR) and Soc(RR). For a module M, E(M) and PE(M) denote the injective and pure-injective envelopes of M, respectively. For a submodule A ⊆ M, the notation A ⊆⊕M will mean that A is a direct summand of M.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 37 , Issue 3 , September 1995 , pp. 373 - 378
Copyright
Copyright © Glasgow Mathematical Journal Trust 1995

References

REFERENCES

1.Camillo, V., Commutative rings whose principal ideals are annihilators, Portugal. Math. 46 (1989), 33–37.Google Scholar
2.Grätzer, G., Lattice theory, (Freeman & Company, 1971).Google Scholar
3.Herzog, I., A test for finite representation type, J. Pure Appl. Alg. 95 (1994), 151–182.CrossRefGoogle Scholar
4.Müller, B. J. and Singh, S., Uniform modules over serial rings, J. Algebra 144 (1991), 94–109.Google Scholar
5.Nicholson, W. K. and Yousif, M. F., Principally injective rings, J. Algebra 174 (1995), 77–93.CrossRefGoogle Scholar
6.Nicholson, W. K. and Yousif, M. F., On completely principally injective rings, Bull. Austral. Math. Soc. 49 (1994), 513–518.CrossRefGoogle Scholar
7.Puninski, G., Pure injective modules over right noetherian serial rings, Comm. Algebra 23 (1995), 1579–1592.CrossRefGoogle Scholar
8.Puninski, G., Prest, M. and Rothmaler, Ph., Rings described by various purities, preprint (1994).Google Scholar
9.Puninski, G. and Wisbauer, R., Σ-pure injective modules over left duo and left distributive rings, preprint (1994).Google Scholar
10.Rutter, E. A., Rings with the principal extension property, Comm. Algebra 3 (1975), 203–212.Google Scholar
11.Warfield, R. B. Jr, Serial rings and finitely presented modules, J. Algebra 37 (1975), 187–222.Google Scholar
12.Wisbauer, R., Foundations of module and ring theory (Gordon and Breach, 1991).Google Scholar
13.Wright, M. H., Right locally distributive rings in Ring theory, (World Scientific, 1993), 350–357.Google Scholar
14.Ming, R. Yue Chi, On injectivity and p-injectivity, J. Math. Kyoto Univ. 27 (1987), 439–452.Google Scholar