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Adjoining an Identity to a Reduced Archimedean f-Ring.
- Source :
-
Communications in Algebra . May2007, Vol. 35 Issue 5, p1487-1503. 17p. - Publication Year :
- 2007
-
Abstract
- Let frA denote the category of f-rings which are reduced and Archimedean, and let Φ be the (nonfull) subcategory of such rings with identity (each with the natural morphisms). Some time ago, the second author showed, using his representation theory, that for each A ∈ | frA| there is a certain minimal embedding uA:A→ uA ∈ | Φ|. More recently, he has revisited the representation theory, expanding it to include the representation of morphisms. Based upon this, the present article analyzes the operator u:| frA| → Φ: the construction of uA is tidied, several characterizations of the pair (uA, uA) are given, and the relation between the maximal ideal structures of A and uA is described. Membership in the class U of frA-morphisms that are "u-extendable" is characterized and it is shown that U = (| frA|,U) is a category in which Φ is a full essentially-reflective subcategory. The frA-objects are characterized for which, respectively, ∀ B(frA(A, B) = U (A, B)), and, ∀ B ≠ 0(frA(B, A) = U(B, A)). [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00927872
- Volume :
- 35
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Communications in Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 25006657
- Full Text :
- https://doi.org/10.1080/00927870601168947