Splitting criteria for modular lattices
| Autor: | L. Aileen Hostinsky |
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| Rok vydání: | 1960 |
| Předmět: | |
| Zdroj: | Proceedings of the American Mathematical Society. 11:23-28 |
| ISSN: | 1088-6826 0002-9939 |
| Popis: | Within the framework of a complete modular lattice two types of criteria for uniform splitting are developed in the first part of this note. One deals with the concept of an 'q-automorphic element, and, under the hypothesis that x is -1-automorphic, it is shown that an endomorphism rq is a uniformly splitting endomorphism of p/0 if and only if rq induces a uniformly splitting endomorphism of p/x. The other type is concerned with the existence of a set of elements which are uniformly split by an endomorphism. In the last section application of this theory of splitting gives a further connection between homomorphisms and direct decompositions. The work is based upon and extends certain previous investigations [2; 3; 4] by the author into this problem. Earlier (see [1]) in group theory criteria similar to the first type have been developed for the existence of complements which are normal subgroups and have been used in studying extension types. The present paper generalizes certain of these results by lattice-theoretical methods not used in [1]. |
| Databáze: | OpenAIRE |
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