An equivalence functor between local vector lattices and vector lattices

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Boulabiar Karim

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Journal: CATEGORIES AND GENERAL ALGEBRAIC STRUCTURES WITH APPLICATIONS Year:2019 | Volume:10 | Issue:1 Page(s): 1-15

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Title

An equivalence functor between local vector lattices and vector lattices

Author(s)

Boulabiar Karim | Issue Writer Certificate

Keywords

CategoryQ4

equivalence functorQ4

maximal idealQ4

local vector latticeQ4

radicalQ4

lattice homomorphismQ4

strong unitQ4

Abstract

We call a local vector lattice any vector lattice with a distinguished positive strong unit and having exactly one maximal ideal (its radical). We provide a short study of local vector lattices. In this regards, some characterizations of local vector lattices are given. For instance, we prove that a vector lattice with a distinguished strong unit is local if and only if it is clean with non no-trivial components. Nevertheless, our main purpose is to prove, via what we call the radical functor, that the Category of all vector lattices and lattice homomorphisms is equivalent to the Category of local vectors lattices and unital (i. e., unit preserving) lattice homomorphisms.

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APA: Copy

Boulabiar, Karim. (2019). An equivalence functor between local vector lattices and vector lattices. CATEGORIES AND GENERAL ALGEBRAIC STRUCTURES WITH APPLICATIONS, 10(1 ), 1-15. SID. https://sid.ir/paper/255419/en

Vancouver: Copy

Boulabiar Karim. An equivalence functor between local vector lattices and vector lattices. CATEGORIES AND GENERAL ALGEBRAIC STRUCTURES WITH APPLICATIONS[Internet]. 2019;10(1 ):1-15. Available from: https://sid.ir/paper/255419/en

IEEE: Copy

Karim Boulabiar, “An equivalence functor between local vector lattices and vector lattices,” CATEGORIES AND GENERAL ALGEBRAIC STRUCTURES WITH APPLICATIONS, vol. 10, no. 1 , pp. 1–15, 2019, [Online]. Available: https://sid.ir/paper/255419/en

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