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Original Articles

Rings with countably many direct summands

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Pages 757-769 | Received 01 Sep 1998, Published online: 27 Jun 2007

References

  • Berberian , S.K. 1972 . Baer ∗ -Rings, Grundlehren Math. Wiss , Vol. 195 , New York : Springer-Verlag . Band
  • Birkenmeier , G.F. , Kim , J.Y. and Park , J.K. 1999 . When is the CS condition hereditary? . Comm. Algebra , 27 : 3875 – 3885 .
  • Chatters , A.W. and Hajarnavis , C.R. 1980 . Rings in which every complemented right ideal is a direct summand . Quart. J. Math , 28 ( 2 ) : 61 – 81 .
  • Chatters , A.W. and Khuri , S.M. 1980 . Endomorphism rings of modules over nonsingular CS-rings . J. London Math. Soc , 21 ( 2 ) : 434 – 444 .
  • Clark , W.E. 1967 . Twisted matrix units semigroup algebras . Duke Math. J , 34 ( 2 ) : 417 – 423 .
  • Dung , N.V. and Smith , P.F. 1992 . Hereditary CS-modules . Math. Scand , 71 ( 2 ) : 173 – 180 .
  • Dung , N.V. , Huynh , D.V. , Smith , P.F. and Wisbauer , R. 1994 . Extending Modules , Harlow : Longman .
  • Goodearl , K.R. 1991 . Von Neumann Regular Rings , Malabar : Krieger .
  • Jacobson , N. 1964 . “ Structure of Rings ” . In Amer. Math. Soc , Vol. 37 , Providence : Colloq. Publ .
  • Jeremy , L. 1971 . “ Sur les modules et anneaux quasi-continus ” . In C. R. Acad. Sci Vol. 37 , 80 – 83 . Paris
  • Kaplansky , I. 1950 . Topological representation of algebras,II . Trans. Amer. Math. Soc , 68 : 62 – 75 .
  • Kaplansky , I. 1955 . Any orthocomplemented complete modular lattice is a continuous geometry . Ann. Math , 61 : 524 – 541 .
  • Kaplansky , I. 1968 . Rings of Operators , New York : Benjamin .
  • Kim , J.Y. and Park , J.K. 1997 . When is a regular ring semisimple Artinian? . Math. Japonica , 45 : 311 – 313 .
  • Lawrence , J. 1977 . A countable self-injective ring is quasi-Frobenius . Proc. Amer. Math. Soc , 65 : 217 – 220 .
  • Mohamed , S.H. and Müller , B.J. 1980 . “ Continuous and Discrete Modules ” . In London Math. Soc , Vol. 147 , Cambridge : Cambridge Univ. Press . Lecture Note
  • Nicholson W.K. Park J.K. Yousif M.F. On simple-injective rings preprint
  • Osofsky , B.L. 1966 . A generalization of quasi-Frobenius rings . J. Algebra , 4 : 373 – 389 .
  • Pollingher , A. and Zaks , A. 1970 . On Baer and quasi-Baer rings . Duke Math. J , 37 : 127 – 138 .
  • Rangaswamy , K.M. 1974 . Regular and Baer rings . Proc. Amer. Math. Soc , 42 : 354 – 358 .
  • Rickart , C.E. 1946 . Banach algebras with an adjoint operation . Ann. Math , 47 : 528 – 550 .
  • Sherman , S. 1950 . “ The second adjoint of a C∗ -algebra ” . In Proc. Intern. Cong. Math Vol. 1 , 470 Cambridge
  • Small , L.W. 1967 . Semihereditary rings . Bull. Amer. Math. Soc , 73 : 656 – 658 .
  • Takeda , Z. 1954 . Conjugate spaces of operator algebras . Proc. Japan Acad , 30 : 90 – 95 .
  • Teply , M.L. 1997 . “ Right hereditary, right perfect rings are semiprimary ” . In Advances in Ring Theory , Edited by: Jain , S.K. and Rizvi , S.T. 313 – 316 . Boston : Birkhäuser .
  • Utumi , Y. 1965 . On continuous rings and self-injective rings . Trans. Amer. Math. Soc , 118 : 158 – 173 .

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