×

Spectra of modules. (English) Zbl 0853.13011

Generalizing the usual notion of spectrum of a ring the author studies spectra of modules. He examines the relationship with the spectrum of the ring and obtains e.g. criteria when the canonical map from the spectrum of a module of the spectrum of the ground ring is surjective or bijective. He also gives an example of a non-zero module with an empty spectrum.

MSC:

13C99 Theory of modules and ideals in commutative rings
13A15 Ideals and multiplicative ideal theory in commutative rings
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] DOI: 10.1016/0021-8693(81)90112-5 · Zbl 0468.13011
[2] Bourbaki N., Algèbre (1958)
[3] Bourbaki N., Algèbre commutative (1961) · Zbl 0108.04002
[4] DOI: 10.1080/00927878808823601 · Zbl 0642.13002
[5] Jain R. K., Riv. Mat. Univ. Parma 7 pp 461– (1981)
[6] Kaplansky I., Commutative rings (1970)
[7] Lee S. C., J. Korean Math. Soc. 28 pp 1– (1991)
[8] Lu C. P., Comment. Math. Univ. St. Paul 33 pp 61– (1984)
[9] Lu C. P., Math. Japon. 34 pp 211– (1989)
[10] DOI: 10.1080/00927879208824432 · Zbl 0776.13007
[11] DOI: 10.1017/CBO9780511565922
[12] Sharp R. Y., Steps in commutative algebra (1990) · Zbl 0703.13001
[13] DOI: 10.1016/0021-8693(75)90074-5 · Zbl 0319.16025
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.