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| Paper IPM / M / 51 |
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| Abstract: | |
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Summand sum property (SSP) and summand intersection property (SIP) of modules are studied in [8] and [15] respectively. In this paper we give some topological characterizations of these properties in C(X). It is shown that the ring C(X) has SIP if and only if every interseciton
of closed-open subsets of X has a closed interior. This characterization then shows that for a large class of topological spaces, such as locally connected spaces and extremally disconnected spaces, the ring C(X) has SIP. It is also shown that C(X) has SSP if and only if the space X has only finitely many components. Finally, using summand ideals of C(X), we will give several algebraic characterizations of some disconnected spaces.
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