Algebraic properties of rings of continuous functions

• Autorzy: M. A. Mulero
• Języki publikacji: EN

Abstrakty

EN

This paper is devoted to the study of algebraic properties of rings of continuous functions. Our aim is to show that these rings, even if they are highly non-noetherian, have properties quite similar to the elementary properties of noetherian rings: we give going-up and going-down theorems, a characterization of z-ideals and of primary ideals having as radical a maximal ideal and a flatness criterion which is entirely analogous to the one for modules over principal ideal domains.

Słowa kluczowe

EN

rings of continuous functions; going-up and going-down theorems; z-ideals; primary ideals; flat modules

Kategorie tematyczne

• 54C40: Algebraic properties of function spaces
• 13C11: Injective and flat modules and ideals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1996
• Tom: 149
• Numer: 1
• Strony: 55-66

Daty

wydano

1996

otrzymano

1995-01-06

poprawiono

1995-09-28

Twórcy

autor

M. A. Mulero

• Departamento de Matemáticas, Universidad de Extremadura, 06071 Badajoz, Spain

Bibliografia

• [1] M. Atiyah and I. G. MacDonald, Introduction to Commutative Algebra, Addison-Wesley, 1969.
• [2] R. Bkouche, Couples spectraux et faisceaux associés. Applications aux anneaux de fonctions, Bull. Soc. Math. France 98 (1970), 253-295.
• [3] N. Bourbaki, Algèbre commutative, Ch. 1 and 2, Hermann, 1961.
• [4] L. Gillman and M. Jerison, Rings of Continuous Functions, Springer, 1976.
• [5] T. Isiwata, Mappings and spaces, Pacific J. Math. 20 (1967), 455-480.
• [6] C. W. Khols, Prime ideals in rings of continuous functions II, Duke Math. J. 2 (1958), 447-458.
• [7] W. S. Massey, Algebraic Topology: An Introduction, Springer, 1967.
• [8] H. Matsumura, Commutative Algebra, 2nd ed., Benjamin, 1980.
• [9] M. A. Mulero Díaz, Revestimientos finitos y álgebras de funciones continuas, Ph.D. Thesis, Univ. de Extremadura, 1992.
• [10] J. Muñoz Díaz, Caracterización de las álgebras diferenciales y síntesis espectral para módulos sobre tales álgebras, Collect. Math. 23 (1972), 17-83.
• [11] C. W. Neville, Flat C(X)-modules and F-spaces, Math. Proc. Cambridge Philos. Soc. 106 (1989), 237-244.