Star-Operations that Distribute Over Finite Intersections

Anderson, Derek T.; Clarke, Sharon M.

doi:10.1081/agb-200063586

Cited by 12 publications

(14 citation statements)

References 11 publications

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“…In Section 4, we study ascents and descents of L-semistar operations, and obtain similar results with the result [15]. In Section 5, we study stability of L-semistar operations, and extend the results [2] and [14] to L-semistar operations. The notion of L-semistar operation seems interesting and essential.…”

Section: Introductionsupporting

confidence: 53%

On generalized Kronecker function rings, II

Okabe

2012

Math. J. Ibaraki Univ.

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Section: Introductionsupporting

confidence: 53%

On generalized Kronecker function rings, II

Okabe

2012

Math. J. Ibaraki Univ.

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“…also (1), (2) and Proposition 5; the "only if " part was proved by Matsuda and Okabe [31], cf. also [3,Theorem 2.8]. )…”

Section: However In the Particular Case That = V Then D Is A V-domamentioning

confidence: 96%

Prüfer ⋆–multiplication domains and ⋆–coherence

Fontana

Picozza

2006

Ricerche mat.

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The purpose of this paper is to deepen the study of the Prüfer -multiplication domains, where is a semistar operation. For this reason, we introduce the -domains, as a natural extension of the v-domains. We investigate their close relation with the Prüfer -multiplication domains. In particular, we obtain a characterization of Prüfer -multiplication domains in terms of -domains satisfying a variety of coherent-like conditions. We extend to the semistar setting the notion of H-domain introduced by Glaz and Vasconcelos and we show, among the other results that, in the class of the H( )-domains, the Prüfer -multiplication domains coincide with the -domains.

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“…A number of authors (Anderson, 1988;Anderson et al, 1989a,b;Anderson and Cook, 2000;Anderson and Clarke, 2005;Fontana and Huckaba, 2000;Garcia et al, 1999;Halter-Koch, 2000, 2001 …”

Section: Star-operationsmentioning

confidence: 98%