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Stipriai pirminiai moduliai virš žiedų / Strongly prime modules over rings

The purpose of this work is to analyse the analogue of prime modules in commutative case – strongly prime modules over rings in non-commutative case. Strongly prime modules over rings, two-sided and one-sided strongly prime ideals in the rings are examined in the work. Concepts and theorems related to this topic are analysed in the paper. These problems are solved: • Taking the homomorphism of the ring R into ring of endomorphisms of the Abelian group we get all the modules over the ring R. • Annihilators of the nonzero elements of the module over commutative ring coincide and are the prime ideal. • In non-commutative case module is strongly prime only in the case when annihilators its nonzero elements are equivalent. • Finite Cartesian product of strongly prime modules, in which annihilators of the nonzero elements are equivalent, is a strongly prime module.

Identiferoai:union.ndltd.org:LABT_ETD/oai:elaba.lt:LT-eLABa-0001:E.02~2005~D_20050623_152837-34895
Date23 June 2005
CreatorsBandalevičiūtė, Marijana
ContributorsBaliukonytė, Stasė, Januškevičius, Romanas, Kaučikas, Algirdas, Mazėtis, Edmundas, Zybartas, Saulius, Vilnius Pedagogical University
PublisherLithuanian Academic Libraries Network (LABT), Vilnius Pedagogical University
Source SetsLithuanian ETD submission system
LanguageLithuanian
Detected LanguageEnglish
TypeMaster thesis
Formatapplication/pdf
Sourcehttp://vddb.library.lt/obj/LT-eLABa-0001:E.02~2005~D_20050623_152837-34895
RightsUnrestricted

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