Congruences and ideals on Boolean modules: a heterogeneous point of view
Definitions for heterogeneous congruences and heterogeneous ideals on a Boolean module M are given and the respective lattices CongM and IdeM are presented. A characterization of the simple Boolean modules is achieved differing from that given by Brink in a homogeneous approach. We construct the sma...
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| Format: | other |
| Language: | eng |
| Published: |
2010
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| Online Access: | http://hdl.handle.net/10316/13651 |
| Country: | Portugal |
| Oai: | oai:estudogeral.sib.uc.pt:10316/13651 |
| Summary: | Definitions for heterogeneous congruences and heterogeneous ideals on a Boolean module M are given and the respective lattices CongM and IdeM are presented. A characterization of the simple Boolean modules is achieved differing from that given by Brink in a homogeneous approach. We construct the smallest and the greatest modular congruence having the same Boolean part. The same is established for modular ideals. The notions of kernel of a modular congruence and the congruence induced by a modular ideal are introduced to describe an isomorphism between CongM and IdeM. This isomorphism leads us to conclude that the class of the Boolean module is ideal determined. |
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