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1	Stipriai pirminiai moduliai virš žiedų / Strongly prime modules over rings Bandalevičiūtė, Marijana 23 June 2005 (has links) 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. 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