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1999 | 160 | 1 | 15-25
Tytuł artykułu

On z◦ -ideals in C(X)

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
An ideal I in a commutative ring R is called a z°-ideal if I consists of zero divisors and for each a ∈ I the intersection of all minimal prime ideals containing a is contained in I. We characterize topological spaces X for which z-ideals and z°-ideals coincide in , or equivalently, the sum of any two ideals consisting entirely of zero divisors consists entirely of zero divisors. Basically disconnected spaces, extremally disconnected and P-spaces are characterized in terms of z°-ideals. Finally, we construct two topological almost P-spaces X and Y which are not P-spaces and such that in every prime z°-ideal is either a minimal prime ideal or a maximal ideal and in C(Y) there exists a prime z°-ideal which is neither a minimal prime ideal nor a maximal ideal.
Słowa kluczowe
Rocznik
Tom
160
Numer
1
Strony
15-25
Opis fizyczny
Daty
wydano
1999
otrzymano
1997-11-20
poprawiono
1998-05-27
poprawiono
1998-07-20
Twórcy
autor
  • Department of Mathematics, Chamran University, Ahvaz, Iran
Bibliografia
  • [1] M. F. Atiyah and I. G. Macdonald, Introduction to Commutative Algebra, Addi-son-Wesley, Reading, Mass., 1969.
  • [2] F. Azarpanah, Essential ideals in , Period. Math. Hungar. 3 (1995), no. 12, 105-112.
  • [3] F. Azarpanah, Intersection of essential ideals in , Proc. Amer. Math. Soc. 125 (1997), 2149-2154.
  • [4] G. De Marco, On the countably generated z-ideals of , ibid. 31 (1972), 574-576.
  • [5] L. Gillman and M. Jerison, Rings of Continuous Functions, Springer, 1976.
  • [6] M. Henriksen and M. Jerison, The space of minimal prime ideals of a commutative ring, Trans. Amer. Math. Soc. 115 (1965), 110-130.
  • [7] C. B. Huijsmans and B. de Pagter, On z-ideals and d-ideals in Riesz spaces. I, Indag. Math. 42 (Proc. Netherl. Acad. Sci. A 83) (1980), 183-195.
  • [8] O. A. S. Karamzadeh, On a question of Matlis, Comm. Algebra 25 (1997), 2717-2726.
  • [9] O. A. S. Karamzadeh and M. Rostami, On the intrinsic topology and some related ideals of , Proc. Amer. Math. Soc. 93 (1985), 179-184.
  • [10] R. Levy, Almost P-spaces, Canad. J. Math. 2 (1977), 284-288.
  • [11] A. I. Veksler, p'-points, p'-sets, p'-spaces. A new class of order-continuous measures and functions, Soviet Math. Dokl. 14 (1973), 1445-1450.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv160i1p15bwm
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