subdirect decomposition
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2017 ◽  
Vol 2017 ◽  
pp. 1-5
Author(s):  
Yizhi Chen ◽  
Jing Tian ◽  
Zhongzhu Liu

Subdirect decomposition of algebra is one of its quite general and important constructions. In this paper, some subdirect decompositions (including subdirect irreducible decompositions) of finite distributive lattices and finite chains are studied, and some general results are obtained.


2016 ◽  
Vol 45 (3/4) ◽  
Author(s):  
Bogdan Staruch ◽  
Bożena Staruch

We describe here a special subdirect decomposition of algebras with modular congruence lattice. Such a decomposition (called a star-decomposition) is based on the properties of the congruence lattices of algebras. We consider four properties of lattices: atomic, atomless, locally uniform and anti-uniform. In effect, we describe a star-decomposition of a given algebra with modular congruence lattice into two or three parts associated to these properties.


2007 ◽  
Vol 57 (3) ◽  
Author(s):  
Ján Jakubík

AbstractThe notion of internal subdirect decomposition can be defined in each variety of algebras. In the present note we prove the validity of a cancellation rule concerning such decompositions for lattice ordered groups and for GMV-algebras. For the case of groups, this cancellation rule fails to be valid.


1992 ◽  
Vol 100 (1) ◽  
pp. 137-156 ◽  
Author(s):  
Daniel Benninger ◽  
Jürg Schmid

1991 ◽  
Vol 34 (1) ◽  
pp. 45-64 ◽  
Author(s):  
Bruno Bosbach

By a divisibility semigroup we mean an algebra (S,., ∧) satisfying (Al) (S,.) is a semigroup; (A2) (S, ∧) is a semilattice; (A3) .A divisibility semigroup is called representable if it admits a subdirect decomposition into totally ordered factors.In this paper various types of representable divisibility semigroups are investigated and characterized, admitting a representation in general or even a special decomposition, like subdirect sums of archimedean factors, for instance.


Author(s):  
Francis Pastijn

AbstractA completely regular semigroup is a semigroup which is a union of groups. The class CR of completely regular semigroups forms a variety. On the lattice L (CR) of completely regular semigroup varieties we define two closure operations which induce complete congruences. The consideration of a third complete congruence on L (CR) yields a subdirect decomposition of L (CR). Using these results we show that L (CR) is arguesian. This confirms the (tacit) conjecture that L (CR) is modular.


1985 ◽  
Vol 13 (2) ◽  
pp. 479-494 ◽  
Author(s):  
T. Anderson ◽  
K. Kaarli ◽  
R. Wiegandt

1983 ◽  
Vol 17 (1) ◽  
pp. 275-287 ◽  
Author(s):  
Rudolf Wille

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