On a cancellation rule for subdirect products of lattice ordered groups and of GMV-algebras

Ján Jakubík

doi:10.2478/s12175-007-0016-5

On a cancellation rule for subdirect products of lattice ordered groups and of GMV-algebras

Mathematica Slovaca ◽

10.2478/s12175-007-0016-5 ◽

2007 ◽

Vol 57 (3) ◽

Cited By ~ 1

Author(s):

Ján Jakubík

Keyword(s):

Present Note ◽

Variety Of Algebras ◽

Subdirect Decomposition ◽

Ordered Groups ◽

Lattice Ordered Groups ◽

Subdirect Products

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.

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Formations of lattice ordered groups and of GMV-algebras

Mathematica Slovaca ◽

10.2478/s12175-008-0091-2 ◽

2008 ◽

Vol 58 (5) ◽

Cited By ~ 7

Author(s):

Ján Jakubík

Keyword(s):

Partially Ordered ◽

Ordered Groups ◽

Lattice Ordered Groups ◽

Infinite Distributivity ◽

Subdirect Products

AbstractA class of lattice ordered groups is called a formation if it is closed with respect to homomorphic images and finite subdirect products. Analogously we define the formation of GMV-algebras. Let us denote by ℱ1 and ℱ2 the collection of all formations of lattice ordered groups or of GMV-algebras, respectively. Both ℱ1 and ℱ2 are partially ordered by the class-theoretical inclusion. We prove that ℱ1 satisfies the infinite distributivity law

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Generalized Commutativity of Lattice-Ordered Groups

Mathematica Slovaca ◽

10.1515/ms-2015-0026 ◽

2015 ◽

Vol 65 (2) ◽

Cited By ~ 1

Author(s):

M. R. Darnel ◽

W. C. Holland ◽

H. Pajoohesh

Keyword(s):

Theorem Proving ◽

Natural Generalization ◽

Ordered Groups ◽

Lattice Ordered Groups ◽

Weak Commutativity

AbstractIn this paper we explore generalizations of Neumann’s theorem proving that weak commutativity in ordered groups actually implies the group is abelian. We show that a natural generalization of Neumann’s weak commutativity holds for certain Scrimger ℓ-groups.

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