Extreme maximal ideals of a partially ordered vector space
نویسندگان
چکیده
منابع مشابه
Extreme Maximal Ideals of a Partially Ordered Vector Space
1. Let F be a partially ordered vector space with an order unit e. It is well known that the class 5DÎ of maximal ideals of V is in one-one correspondence with the class K of normalized positive linear functionals, in the sense that to each ME^SR corresponds a positive linear functional <¡>m with M as its null-space and with M(e) = 1. A maximal ideal MG 90? is said to be extreme if <pM is an...
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Pseudoeffect algebras are non-commutative generalizations of effect algebras, which can serve as models of both quantum structures and non-commutative logics. The main contribution of this study is twofold. Firstly, we initiate an order-theoretic extension of pseudoeffect algebras, called partially ordered pseudoeffect algebras (abbreviated po-PEAs). Secondly, we investigate the fuzzy ideal the...
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The rings considered in this article are commutative with identity $1neq 0$. By a proper ideal of a ring $R$, we mean an ideal $I$ of $R$ such that $Ineq R$. We say that a proper ideal $I$ of a ring $R$ is a maximal non-prime ideal if $I$ is not a prime ideal of $R$ but any proper ideal $A$ of $R$ with $ Isubseteq A$ and $Ineq A$ is a prime ideal. That is, among all the proper ideals of $R$,...
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The Hahn-Banach theorem is one of the most fundamental theorems in the functional analysis theory. This theorem is well known in the case where the range space is the real number system as follows. Let p be a sublinear mapping from a vector space X into the real number system R, Y a subspace of X, and q a linear mapping from Y into R such that q ≤ p on Y. Then there exists a linear mapping g fr...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1956
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1956-0080883-1