Congruences and ideals on Boolean modules: a heterogeneous point of view
نویسندگان
چکیده
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.
منابع مشابه
Congruences and ideals on Peirce algebras: a heterogeneous/homogeneous point of view
For a Peirce algebra P, lattices CongP of all heterogenous Peirce congruences and IdeP of all heterogenous Peirce ideals are presented. The notions of kernel of a Peirce congruence and the congruence induced by a Peirce ideal are introduced to describe an isomorphism between CongP and IdeP. This isomorphism leads us to conclude that the class of the Peirce algebras is ideal determined. Opposed ...
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عنوان ژورنال:
- Math. Log. Q.
دوره 57 شماره
صفحات -
تاریخ انتشار 2011