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2000 | 83 | 1 | 5-13
Tytuł artykułu

On the maximal spectrum of commutative semiprimitive rings

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The space of maximal ideals is studied on semiprimitive rings and reduced rings, and the relation between topological properties of Max(R) and algebric properties of the ring R are investigated. The socle of semiprimitive rings is characterized homologically, and it is shown that the socle is a direct sum of its localizations with respect to isolated maximal ideals. We observe that the Goldie dimension of a semiprimitive ring R is equal to the Suslin number of Max(R).
Słowa kluczowe
Rocznik
Tom
83
Numer
1
Strony
5-13
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-01-15
poprawiono
1999-07-19
Twórcy
autor
  • Department of Mathematics, University of Bu-Ali Sina, Hamadan, Iran
Bibliografia
  • [1] M. Contessa, On PM-rings, Comm. Algebra 10 (1982), 93-108.
  • [2] G. De Marco and A. Orsatti, Commutative rings in which every prime ideal is contained in a unique maximal ideal, Proc. Amer. Math. Soc. 30 (1971), 459-466.
  • [3] R. Engelking, General Topology, PWN-Polish Sci. Publ., 1977.
  • [4] L. Gillman, Rings with Hausdorff structure space, Fund. Math. 45 (1957), 1-16.
  • [5] M. Henriksen and M. Jerison, The space of minimal prime ideals of a commutative ring, Trans. Amer. Math. Soc. 115 (1965), 110-130.
  • [6] O. A. S. Karamzadeh and M. Rostami, On the intrinsic topology and some related ideals of C(X), Proc. Amer. Math. Soc. 93 (1985), 179-184.
  • [7] C. W. Kohls, The space of prime ideals of a ring, Fund. Math. 45 (1957), 17-27.
  • [8] G. Mason, z-ideals and prime ideals, J. Algebra 26 (1973), 280-297.
  • [9] J. C. McConnell and J. C. Robson, Noncommutative Noetherian Rings, Wiley Interscience, New York, 1987.
  • [10] S. H. Sun, Noncommutative rings in which every prime ideal is contained in a unique maximal ideal, J. Pure Appl. Algebra 76 (1991), 179-192.
  • [11] S. H. Sun, Rings in which every prime ideal is contained in a unique maximal ideal, ibid. 78 (1992), 183-194.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv83i1p5bwm
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