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    Puninski, G. E. 2012. Pure projective modules over exceptional uniserial noncoherent rings. Journal of Mathematical Sciences, Vol. 187, Issue. 2, p. 157.
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On p-injective rings

  • Gennadi Puninski (a1), Robert Wisbauer (a2) and Mohamed Yousif (a3)
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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.

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COPYRIGHT: © Glasgow Mathematical Journal Trust 1995
References
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1.Camillo, V., Commutative rings whose principal ideals are annihilators, Portugal. Math. 46 (1989), 33–37.
2.Grätzer, G., Lattice theory, (Freeman & Company, 1971).
3.Herzog, I., A test for finite representation type, J. Pure Appl. Alg. 95 (1994), 151–182.
4.Müller, B. J. and Singh, S., Uniform modules over serial rings, J. Algebra 144 (1991), 94–109.
5.Nicholson, W. K. and Yousif, M. F., Principally injective rings, J. Algebra 174 (1995), 77–93.
6.Nicholson, W. K. and Yousif, M. F., On completely principally injective rings, Bull. Austral. Math. Soc. 49 (1994), 513–518.
7.Puninski, G., Pure injective modules over right noetherian serial rings, Comm. Algebra 23 (1995), 1579–1592.
8.Puninski, G., Prest, M. and Rothmaler, Ph., Rings described by various purities, preprint (1994).
9.Puninski, G. and Wisbauer, R., Σ-pure injective modules over left duo and left distributive rings, preprint (1994).
10.Rutter, E. A., Rings with the principal extension property, Comm. Algebra 3 (1975), 203–212.
11.Warfield, R. B. Jr, Serial rings and finitely presented modules, J. Algebra 37 (1975), 187–222.
12.Wisbauer, R., Foundations of module and ring theory (Gordon and Breach, 1991).
13.Wright, M. H., Right locally distributive rings in Ring theory, (World Scientific, 1993), 350–357.
14.Ming, R. Yue Chi, On injectivity and p-injectivity, J. Math. Kyoto Univ. 27 (1987), 439–452.
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Glasgow Mathematical Journal
  • ISSN: 0017-0895
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