State radical ideals in state MV -algebras

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Forouzesh F.; Emamipour B.

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Journal Paper

Paper Information

Journal: JOURNAL OF ALGEBRAIC HYPERSTRUCTURES AND LOGICAL ALGEBRAS Year:2024 | Volume:5 | Issue:2 Page(s): 153-167

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Information Journal Paper

Title

State radical ideals in state MV -algebras

Author(s)

Forouzesh F. | Emamipour B. | Issue Writer Certificate

Keywords

Infinitesimal

state ideal

prime state ideal

state radical

state semi-maximal ideal

Abstract

In this paper, the notions of prime state ideals and state semi-maximal ideals of state MV -algebras are introduced. We prove prime state ideal theorem and we show that a state MV -algebra A is semi-simple if and only if A has no state Infinitesimals. We introduce the concept of state radical of state ideals in a state MV -algebra, we present a characterization of a state radical ideal. We show that the set of state radicals of state ideals in (A, σ) is a Heyting algebra.

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