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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.

- R. RAPHAEL, R. G. WOODS
- 2005

Storrer introduced the epimorphic hull of a commutative semiprime ring R and showed that it is (up to isomorphism) the unique essential epic von Neumann regular extension of R. In the case when R = C(X) with X a Tychonoff space, we show that the embedding induced by a dense subspace of X is always essential. This simplifies the search for spaces whose… (More)

- R Raphael
- 1999

A von Neumann regular extension of a semiprime ring naturally deenes a epimorphic extension in the category of rings. These are studied, and four natural examples are considered, two in commutative ring theory, and two in rings of continuous functions.

- R. Raphael, R. G. Woods
- 2004

We continue the study of a lattice-ordered ring G(X), associated with the ring C(X). Following [10], X called RG when G(X) = C(Xδ). An RG-space must have a dense set of very weak P-points. It must have a dense set of almost-P-points if Xδ is Lindelöf, or if the continuum hypothesis holds and C(X) has small cardinality. Space which are RG must have finite… (More)

We study and, in a number of cases, classify completely the limit closures in the category of commutative rings of subcategories of integral domains.

- W D Burgess, R Raphael
- 2006

Given a topological space X, K(X) denotes the upper semi-lattice of its (Hausdorff) compactifications. Recent studies have asked when, for αX ∈ K(X), the restriction homomorphism ρ : C(αX) → C(X) is an epimorphism in the category of commutative rings. This article continues this study by examining the sub-semilattice, Kepi(X), of those compactifications… (More)

1 M.Tech CS&IS ICET, Mulavoor Ernakulam, India 2 Asst. Professor, IT ICET, Mulavoor Ernakulam, India Emailrenithar@gmail.com, chithrarajbhavan@gmail.com ABSTRACT Smart phones and wireless networks have become very popular. Media content has become the major traffic on Internet and can be obtained easily using mobile devices. The availability of the… (More)

We continue our investigations into absolute CR-epic spaces. Given a continuous function f : X // Y , with X absolute CR-epic, we search for conditions which imply that Y is also absolute CR-epic. We are particularly interested in the cases when X is a dense subset of Y and when f is a quotient mapping. To answer these questions, we consider issues of local… (More)

- R. Raphael, Huaxin Lin, Shuang Zhang
- 1999

For any (unital) exchange ring R whose finitely generated projective modules satisfy the separative cancellation property (A ⊕ A ∼= A ⊕ B ∼= B ⊕ B =⇒ A ∼= B), it is shown that all invertible square matrices over R can be diagonalized by elementary row and column operations. Consequently, the natural homomorphism GL1(R) → K1(R) is surjective. In combination… (More)

- R Raphael, R Grant Woods
- 2006

If X is a Tychonoff space then its P -coreflection Xδ is a Tychonoff space that is a dense subspace of the realcompact space (υX)δ, where υX denotes the Hewitt realcompactification of X. We investigate under what conditions Xδ is C-embedded in (υX)δ, i.e. under what conditions υ(Xδ) = (υX)δ. An example shows that this can fail for the product of a compact… (More)