Goldie extending elements in modular lattices.

Autor:	Nimbhorkar, Shriram K.
Další autoři:	Shroff, Rupal C.
Jazyk:	angličtina
Předmět:	matematika mathematics články journal articles modular lattice Goldie extending element
Druh dokumentu:	Non-fiction
ISSN:	0862-7959
Abstrakt:	Abstract: The concept of a Goldie extending module is generalized to a Goldie extending element in a lattice. An element a of a lattice L with 0 is said to be a Goldie extending element if and only if for every b leq a there exists a direct summand c of a such that b wedge c is essential in both b and c. Some properties of such elements are obtained in the context of modular lattices. We give a necessary condition for the direct sum of Goldie extending elements to be Goldie extending. Some characterizations of a decomposition of a Goldie extending element in such a lattice are given. The concepts of an a-injective and an a-ejective element are introduced in a lattice and their properties related to extending elements are discussed.
Databáze:	Katalog Knihovny AV ČR
Externí odkaz:	Plný text