Notes on R1-ideals in partial abelian monoids |
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Authors: | Jenča Gejza |
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Institution: | (1) Department of Mathematics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology, Ilkovičova 3, 812 19 Bratislava, Slovakia, e-mail: jenca@kmat.elf.stuba.sk, SK |
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Abstract: | In the present paper, we deal with a class of R
1-ideals of cancellative positive partial abelian monoids (CPAMs). We prove that, for I being an R
1-ideal of a CPAM P, P/I is a CPAM. The lattice of congruence relations associated with R
1-ideals is a sublattice of the lattice of all equivalence relations. Finally, we prove that an intersection of two Riesz ideals
is a Riesz ideal and that the lattice of Riesz ideals is a sublattice of the lattice of all ideals.
Received March 19, 1999; accepted in final form December 16, 1999. |
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Keywords: | and phrases: Partial semigroup generalized effect algebra |
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