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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
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[1] DOI: 10.1016/0021-8693(81)90112-5 · Zbl 0468.13011 · doi:10.1016/0021-8693(81)90112-5
[2] Bourbaki N., Algèbre (1958)
[3] Bourbaki N., Algèbre commutative (1961) · Zbl 0108.04002
[4] DOI: 10.1080/00927878808823601 · Zbl 0642.13002 · doi:10.1080/00927878808823601
[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 · doi:10.1080/00927879208824432
[11] DOI: 10.1017/CBO9780511565922 · 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 · doi:10.1016/0021-8693(75)90074-5
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