Base and Weight of Boolean I-Contact Algebras

Estaji, Ali Akbar; Ostad, Javad Farokhi; Haghdadi, Toktam

doi:10.1007/s41980-021-00583-x

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2021

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“…This research has been continued by the authors in [26]. The work contains some results concerning the weight of ICAs.…”

Section: Introductionmentioning

confidence: 99%

Topobooleans and Boolean contact algebras with interpolation property

Estaji

Haghdadi

Ostad

2021

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In this paper we study the connections between topobooleans [A.A. Estaji, A. Karimi Feizabadi, and M. Zarghani, Categ. Gen. Algebr. Struct. Appl. 4 (2016), 75-94] and Boolean contact algebras with the interpolation property (briefly, ICAs) [G. Dimov and D. Vakarelov, Fund. Inform. 74 (2006), 209-249]. We prove that every complete ICA generates a topoboolean and, conversely, if a topoboolean satisfies some natural conditions then it generates a complete ICA which, in turn, generates it. We introduce the category ICA of ICAs and suitable morphisms between them. We show that the category ICA has products and every ICA-monomorphism is an injective function. We prove as well that if A and B are complete Boolean algebras, f : B1 ? B2 is a complete Boolean homomorphism and (A,C) is an ICA, then B possesses a final ICA-structure in respect of f.

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“…This research has been continued by the authors in [26]. The work contains some results concerning the weight of ICAs.…”

Section: Introductionmentioning

confidence: 99%