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Title: New operations on partial Abelian monoids defined by preideals (English)
Author: Vinceková, Elena
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 44
Issue: 3
Year: 2008
Pages: 441-450
Summary lang: English
Category: math
Summary: We consider partial abelian monoids, in particular generalized effect algebras. From the given structures, we construct new ones by introducing a new operation $\oplus $, which is given by restriction of the original partial operation + with respect to a special subset called preideal. We bring some derived properties and characterizations of these new built structures, supporting the results by illustrative examples. (English)
Keyword: partial abelian monoid
Keyword: generalized effect algebra
Keyword: preideal
Keyword: Riesz decomposition property
Keyword: central element
MSC: 08A55
MSC: 81P10
idZBL: Zbl 1154.81305
idMR: MR2436043
Date available: 2009-09-24T20:36:20Z
Last updated: 2012-06-06
Stable URL:
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Reference: [3] Hedlíková J., Pulmannová S.: Generalized difference posets and orthoalgebras.Acta Math. Univ. Comenian. 45 (1996), 247–279 Zbl 0922.06002, MR 1451174
Reference: [4] Pulmannová S., Vinceková E.: Riesz ideals in generalized effect algebras and in their unitizations.Algebra Universalis 57 (2007), 4, 393–417 Zbl 1139.81007, MR 2373250
Reference: [5] Riečanová Z., Marinová I.: Generalized homogeneous, prelattice and MV-effect algebras.Kybernetika 41 (2005), 2, 129–142 MR 2138764


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