| 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. |
