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Strongly prime ideals and strongly zero-dimensional rings
Stockholm University, Faculty of Science, Department of Mathematics.
2017 (English)In: Journal of Algebra and its Applications, ISSN 0219-4988, E-ISSN 1793-6829, Vol. 16, no 10, article id 1750191Article in journal (Refereed) Published
Abstract [en]

A prime ideal p is said to be strongly prime if whenever p contains an intersection of ideals, p contains one of the ideals in the intersection. A commutative ring with this property for every prime ideal is called strongly zero-dimensional. Some equivalent conditions are given and it is proved that a zero-dimensional ring is strongly zero-dimensional if and only if the ring is quasi-semi-local. A ring is called strongly n-regular if in each ideal a, there is an element a such that x=ax for all x ∈ an. Connections between the concepts strongly zero-dimensional and strongly n-regular are considered.

Place, publisher, year, edition, pages
2017. Vol. 16, no 10, article id 1750191
Keyword [en]
Prime ideal, zero-dimensional ring, intersections of ideals, strongly prime, strongly zero-dimensional, strongly, n-regular ring
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-138937DOI: 10.1142/S0219498817501912ISI: 000411342000011OAI: oai:DiVA.org:su-138937DiVA, id: diva2:1069935
Available from: 2017-01-30 Created: 2017-01-30 Last updated: 2017-10-16Bibliographically approved

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