Document Zbl 1431.13013

Trivial extensions subject to semi-regularity and semi-coherence. (English) Zbl 1431.13013

Quaest. Math. 43, No. 1, 45-54 (2020).

Authors’ abstract: In this paper, we investigate the transfer of Matlis’ semi-regularity and semi-coherence in trivial ring extensions issued from rings (with zero-divisors). We use the obtained results to enrich the literature with new examples of semi-regular or semi-coherent rings issued as trivial extensions and validate some questions left open in the literature.

Reviewer: François Couchot (Caen)

Cited in 5 Documents

MSC:

13C10	Projective and free modules and ideals in commutative rings
13C11	Injective and flat modules and ideals in commutative rings
13E05	Commutative Noetherian rings and modules
13F05	Dedekind, Prüfer, Krull and Mori rings and their generalizations
13H10	Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)

Keywords:

trivial ring extension; idealization; semi-regular ring; if ring; coherent ring; semi-coherent ring; arithmetical ring; chained ring; quasi-Frobenius ring; von Neumann regular ring

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References:

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