EMV-Algebras—Extended MV-Algebras

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F21%3A73609920" target="_blank" >RIV/61989592:15310/21:73609920 - isvavai.cz</a>

Výsledek na webu

<a href="https://obd.upol.cz/id_publ/333189807" target="_blank" >https://obd.upol.cz/id_publ/333189807</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-030-52163-9_7" target="_blank" >10.1007/978-3-030-52163-9_7</a>

Jazyk výsledku

angličtina

Název v původním jazyce

EMV-Algebras—Extended MV-Algebras

Popis výsledku v původním jazyce

The present paper is a survey on a new kind of algebras, called EMV-algebras, generalizing both MV-algebras and generalized Boolean algebras. The survey is based on our papers[10–13]. For these algebras a top element is not assumed a priori. Every EMV-algebra can be covered by a system of MV-algebras where each of them uses the restriction of ⊕, ∨, ∧. We prove that every such an EMV-algebra without top element can be embedded into an EMV-algebra with top element as its maximal ideal, and every EMV-algebra with top element is termwise equivalent to an MV-algebra. We show that the classes of EMV-algebras are intimately connected with subvarieties of MV-algebras. We establish a categorical equivalence of the category of EMV-algebras without top element with a special category of MV-algebras. We will study states and state-morphisms, their topological properties, a Krein–Mil’man-type representation, and an integral representation. We show also a kind of the Loomis–Sikorski theorem. Finally, we present some results on free EMV-algebras.

Název v anglickém jazyce

EMV-Algebras—Extended MV-Algebras

Popis výsledku anglicky

The present paper is a survey on a new kind of algebras, called EMV-algebras, generalizing both MV-algebras and generalized Boolean algebras. The survey is based on our papers[10–13]. For these algebras a top element is not assumed a priori. Every EMV-algebra can be covered by a system of MV-algebras where each of them uses the restriction of ⊕, ∨, ∧. We prove that every such an EMV-algebra without top element can be embedded into an EMV-algebra with top element as its maximal ideal, and every EMV-algebra with top element is termwise equivalent to an MV-algebra. We show that the classes of EMV-algebras are intimately connected with subvarieties of MV-algebras. We establish a categorical equivalence of the category of EMV-algebras without top element with a special category of MV-algebras. We will study states and state-morphisms, their topological properties, a Krein–Mil’man-type representation, and an integral representation. We show also a kind of the Loomis–Sikorski theorem. Finally, we present some results on free EMV-algebras.

Druh

C - Kapitola v odborné knize

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název knihy nebo sborníku

Trends in Logic

ISBN

978-3-030-52162-2

Počet stran výsledku

26

Strana od-do

107-132

Počet stran knihy

493

Název nakladatele

Springer

Místo vydání

Cham

Kód UT WoS kapitoly

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