Stipriai pirminiai moduliai virš žiedų

• Main Author: Bandalevičiūtė, Marijana
• Other Authors: Baliukonytė, Stasė
• Format: Dissertation
• Language: Lithuanian
• Published: Lithuanian Academic Libraries Network (LABT) 2005
• Subjects: Mathematics; Kvaziinjektyvus modulis virš žiedo R; Pomodulio esminis plėtinys; Stipriai pirminis modulis; Annihiliator; Homomorphism of the ring R; Modulio plėtinys; Strongly prime modules over rings; Pomodulis; Žiedas; Žiedų homomorfizmas; Ring; Žiedo R modulio injektyvus apvalkalas; Kairiųjų R-modulių homomorfizmas; Idealas; Ideal; Anuliatorius; Faktormodulis; Modules
• Online Access: http://vddb.library.lt/fedora/get/LT-eLABa-0001:E.02~2005~D_20050623_152837-34895/DS.005.0.02.ETD

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.