On the lattice of basic z^{\circ}–ideals
Ali Taherifar\,
Department of Mathematics, Yasouj University, Yasouj, Iran.
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Pages 268-274 | Received 02 February 2025, Accepted 21 May 2025, Published 04 January 2026
Abstract
It has been shown that for a reduced f-ring R with bounded inversion property, the lattice of basic z^{\circ}-ideals is a complemented lattice if and only if the space of minimal prime ideals, Min(R), is compact and R satisfies the annihilator condition. Examples are provided to illustrate and delineate these results.
Keywords: Commutative ring, z-ideal, ring of continuous functions, reduced ring.
MSC numbers: 13A15, 16G30, 54C40.
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