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.
| Identifer | oai:union.ndltd.org:LABT_ETD/oai:elaba.lt:LT-eLABa-0001:E.02~2005~D_20050623_152837-34895 |
| Date | 23 June 2005 |
| Creators | Bandalevičiūtė, Marijana |
| Contributors | Baliukonytė, Stasė, Januškevičius, Romanas, Kaučikas, Algirdas, Mazėtis, Edmundas, Zybartas, Saulius, Vilnius Pedagogical University |
| Publisher | Lithuanian Academic Libraries Network (LABT), Vilnius Pedagogical University |
| Source Sets | Lithuanian ETD submission system |
| Language | Lithuanian |
| Detected Language | English |
| Type | Master thesis |
| Format | application/pdf |
| Source | http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2005~D_20050623_152837-34895 |
| Rights | Unrestricted |
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