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Information Journal Paper

Title

State extended ideals in state MV-algebras

Pages

  187-201

Abstract

 In this paper, we introduce the notion of state extended ideal associated to a subset of state MV-algebras and investigate the related properties. A characterization of this state extended ideal in a state MV-algebras is given. In addition, we study the relation between state extended ideals and state prime ideals, state maximal ideal in a state MV-algebra. We show that if f: A→ B is state homomorphism MV-algebra such that f(A^' )=B', then we have (1) If I is a state stable relative to B'⊆ B, then f^(-1) (I) is a state stable relative to A'⊆ A. (2) If f is an onto and I is a state stable relative to A'⊆ A, Ker(f)⊆ I, then f(I) is a state stable relative to B'⊆ B. In finally, we define state stable ideals and we show that the class S(B) of all state stable ideals relative to B⊆ A is also a complete Heyting algebra, for a state MV-algebra (A, σ ).

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    • Cite

    APA: Copy

    FOROUZESH, FERESHTEH, Dehghani Poshtroudi, zahra, Waezizadeh, Tayebeh, & EBRAHIMPOUR, MAHDIEH. (2021). State extended ideals in state MV-algebras. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 7(30 ), 187-201. SID. https://sid.ir/paper/952717/en

    Vancouver: Copy

    FOROUZESH FERESHTEH, Dehghani Poshtroudi zahra, Waezizadeh Tayebeh, EBRAHIMPOUR MAHDIEH. State extended ideals in state MV-algebras. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2021;7(30 ):187-201. Available from: https://sid.ir/paper/952717/en

    IEEE: Copy

    FERESHTEH FOROUZESH, zahra Dehghani Poshtroudi, Tayebeh Waezizadeh, and MAHDIEH EBRAHIMPOUR, “State extended ideals in state MV-algebras,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 7, no. 30 , pp. 187–201, 2021, [Online]. Available: https://sid.ir/paper/952717/en

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