Lattice-Ordered Injective Hulls
نویسندگان
چکیده
منابع مشابه
Injective Hulls of Partially Ordered Monoids
We find the injective hulls of partially ordered monoids in the category whose objects are po-monoids and submultiplicative order-preserving functions. These injective hulls are with respect to a special class of monics called “embeddings”. We show as well that the injective objects with respect to these embeddings are precisely the quantales.
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Proof. The idempotents correspond to the Borel sets modulo sets of first category. Since, in addition, the idempotents generate B(X), B(X) is an AW* and hence an injective algebra. The natural map U of C(X) into B(X) induced by the inclusion map is clearly a homomorphism. It is one-one since continuous functions which are not identically equal must differ on a set of second category. To complet...
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We define in this paper a certain notion of completeness for a wide class of commutative (pre)ordered monoids (from now on P.O.M.’s). This class seems to be the natural context for studying structures like measurable function spaces, equidecomposability types of spaces, partially ordered abelian groups and cardinal algebras. Then, we can prove that roughly speaking, spaces of measures with valu...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1972
ISSN: 0002-9947
DOI: 10.2307/1996249