On Topological Spaces X Determined by the Torsion Elements of C(X)

Ali Rezaei Aliabad, Mansoor Motamedi

Abstract


Let C(X) be the ring of real continuous functions on aTychonoff space X and T(X) be the set of all torsion elements of C(X).We prove that if X and Y are two zero dimensional compact spaces,then X ' Y if and only if the rings generated by T(X) and T(Y ) areisomorphic.

Keywords


Group of units of C(X), torsion subgroup, socle of a group, maximal subgroup, Frattini subgroup, P-filter, Pultrafilter

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