Primary decompositions in lattices

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 1994 English Publisher:Springer Science and Business Media LLCJournal:Algebra Universalis, volume 32, pages 307-313 (issn: 0002-5240, eissn: 1420-8911,

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Authors: Stern, J. A.;

doi: 10.1007/bf01235172

Primary decompositions in lattices

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Abstract

A general definition of primary theory for semilattices is given which generalizes all known decompositions in noncommutative rings and multiplicative lattices. It is proved that there exist minimal primary decompositions. The author gives a new notion of radicals for semilattices, which have properties similar to the nilpotent radicals of commutative rings.

Keywords

primary theory, semilattices, Semilattices, minimal primary decompositions, radicals

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