The Lexicographic Product of Po-groups and n-Perfect Pseudo Effect Algebras
نویسندگان
چکیده
منابع مشابه
THE LEXICOGRAPHIC PRODUCT OF PO-GROUPS AND n-PERFECT PSEUDO EFFECT ALGEBRAS
We will study the existence of different types of the Riesz Decomposition Property for the lexicographic product of two partially ordered groups. A special attention will be paid to the lexicographic product of the group of the integers with an arbitrary po-group. Then we apply these results to the study of n-perfect pseudo effect algebras. We show that the category of strong n-perfect pseudo-e...
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We study the Riesz decomposition property types of the lexicographic product of two po-groups. Then we apply them to the study of pseudo effect algebras which can be decomposed into a comparable system of non-void slices indexed by some subgroup of real numbers. Finally, we present their representation by the lexicographic product.
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We introduce perfect effect algebras and we show that every perfect algebra is an interval in the lexicographical product of the group of all integers with an Abelian directed interpolation po-group. To show this we introduce prime ideals of effect algebras with the Riesz decomposition property (RDP). We show that the category of perfect effect algebras is categorically equivalent to the catego...
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ژورنال
عنوان ژورنال: International Journal of Theoretical Physics
سال: 2013
ISSN: 0020-7748,1572-9575
DOI: 10.1007/s10773-013-1568-5