Finite frames, P-frames and basically disconnected frames

Acharyya, Sudip Kumar; Bhunia, Goutam; Ghosh, Partha Pratim

doi:10.1007/s00012-014-0296-x

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Corollary 421

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Cited by 6 publications

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“…It is shown that the pointfree version of this result is also true (see [6]). If we apply the proof of [23,Lemma 4.8] word-for-word, we obtain the following for R c L. In proof of Proposition 4.6, we use this fact: Let J, J be two ideals. If J ∩ J is prime then either J ⊆ J or J ⊆ J.…”

Section: Corollary 42mentioning

confidence: 99%

zc-ideals and prime ideals in the ring RcL

Estaji¹,

Feizabadi²,

Sarpoushi³

2018

Filomat

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The ring R c L is introduced as a sub-f-ring of RL as a pointfree analogue to the subring C c (X) of C(X) consisting of elements with the countable image. We introduce z c-ideals in R c L and study their properties. We prove that for any frame L, there exists a space X such that βL OX with C c (X) R c (OX) R c βL R * c L, and from this, we conclude that if α, β ∈ R c L, |α| ≤ |β| q for some q > 1, then α is a multiple of β in R c L. Also, we show that IJ = I ∩ J whenever I and J are z c-ideals. In particular, we prove that an ideal of R c L is a z c-ideal if and only if it is a z-ideals. In addition, we study the relation between z c-ideals and prime ideals in R c L. Finally, we prove that R c L is a Gelfand ring.

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Section: Corollary 42mentioning

confidence: 99%