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Karim, D.

Zero-dimensional imbeddability. (English) Zbl 1101.13007

Commun. Algebra 34, No. 3, 931-938 (2006).
Every noetherian ring is imbeddable into a 0-dimensional ring. M. Arapovi [Glas. Mat. Ser. III 18(38), 53–59 (1983; Zbl 0521.13005)] gave a general criterion for this kind of imbeddability in the case of arbitrary commutative rings. The author reformulates Arapovich’s theorem with the help of the index of idempotence. Moreover, he studies imbeddability into particular 0-dimensional rings such as quasi-local rings, rings having a finite spectrum and Nagata rings.
Reviewer: Martin Kreuzer (Dortmund)

MSC:

13A99 General commutative ring theory
13A15 Ideals and multiplicative ideal theory in commutative rings
13B02 Extension theory of commutative rings
13E05 Commutative Noetherian rings and modules

Keywords:

locally chained ring; minimal zero-dimensional ring; Nagata ring

Citations:

Zbl 0521.13005
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Full Text: DOI

References:

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[3] Arapovic M., Glas. Mat. Ser. III 18 pp 53– (1983)
[4] Gilmer R., Zero-Dimensional Commutative Rings pp 27– (1995) · Zbl 0859.13005
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[6] DOI: 10.1090/S0002-9939-1992-1095223-0 · doi:10.1090/S0002-9939-1992-1095223-0
[7] DOI: 10.2307/2154348 · Zbl 0778.13012 · doi:10.2307/2154348
[8] Huckaba J., Commutative Rings with Zero Divisors (1988) · Zbl 0637.13001
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