The epimorphic hull of C(X)

✍ Scribed by Robert M. Raphael; R.Grant Woods

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 205 KB
• Volume: 105
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(99)00036-x

✦ Synopsis

The epimorphic hull H (A) of a commutative semiprime ring A is defined to be the smallest von Neumann regular ring of quotients of A.

Let X denote a Tychonoff space. In this paper the structure of H (C(X)) is investigated, where C(X) denotes the ring of continuous real-valued functions with domain X. Spaces X that have a regular ring of quotients of the form C(Y ) are characterized, and a "minimum" such Y is found. Necessary conditions for H (C(X)) to equal C(Y ) for some Y are obtained.