List of Articles ‎MV-algebra

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  1 - State extended ideals in state MV-algebras
  Fereshteh Forouzesh zahra Dehghani Poshtroudi Tayebeh Waezizadeh Mahdieh Ebrahimpour
  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&lrm More

  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). Manuscript profile
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  2 - (Para) topological pseudo mV-algebras
  Nader Kouhestani frazaneh rajabi stodeh beheshteh miri
  10.30495/jnrm.2022.60725.2114
  In the paper, we introduce the notins of PMV-norm on pseudo MV-algebras and study some it’s algebraic properties. We also show that there is a contrvariant functor of pseudo MV-algebras to category of semigroups. We define (para) topological pseudo MV-algebras and More

  In the paper, we introduce the notins of PMV-norm on pseudo MV-algebras and study some it’s algebraic properties. We also show that there is a contrvariant functor of pseudo MV-algebras to category of semigroups. We define (para) topological pseudo MV-algebras and find the connection between them and PMV-pseduo norms. Finally, we define filter topology on this algebraic structure and show that it is a paratopological pseudo MV-algebra. Manuscript profile
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  3 - The category of L-algebras
  Lavinia Corina Ciungu
  10.30495/tfss.2022.1959857.1034
  In this paper, we define and study the category of L-algebras, proving that this category has equalizers, coequalizers, kernel pairs and products. We investigate the existence of injective objects in this category and show that an object in the subcategory of cyclic L-a More

  In this paper, we define and study the category of L-algebras, proving that this category has equalizers, coequalizers, kernel pairs and products. We investigate the existence of injective objects in this category and show that an object in the subcategory of cyclic L-algebras is injective if and only if it is a complete and divisible cyclic L-algebra. Manuscript profile
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  4 - Forensic Dynamic Lukasiewicz Logic
  Antonio Di Nola Revaz Grigolia
  10.30495/tfss.2022.1959658.1035
  A forensic dynamic $n$-valued {\L}ukasiewicz logic $FD{\L}_n$ is introduced on the base of $n$-valued {\L}ukasiewicz logic ${\L}_n$ and corresponding to it forensic dynamic $MV_n$-algebra ($FDL_n$-algebra)‎, ‎$1 < n < \omega$‎, ‎which are algebraic counterparts of the More

  A forensic dynamic $n$-valued {\L}ukasiewicz logic $FD{\L}_n$ is introduced on the base of $n$-valued {\L}ukasiewicz logic ${\L}_n$ and corresponding to it forensic dynamic $MV_n$-algebra ($FDL_n$-algebra)‎, ‎$1 < n < \omega$‎, ‎which are algebraic counterparts of the logic‎, ‎that in turn represent two-sorted algebras $(\mathcal{M}‎, ‎\mathcal{R}‎, ‎\Diamond)$ that combine the varieties of $MV_n$-algebras $\mathcal{M} = (M‎, ‎\oplus‎, ‎\odot‎, ‎\sim‎, ‎0,1)$ and regular algebras $\mathcal{R} = (R,\cup‎, ‎;‎, ‎^\ast)$ into a single finitely axiomatized variety resemblig $R$-module with‎ ‎"scalar"‎ ‎multiplication $\Diamond$‎. ‎Kripke semantics is developed for forensic dynamic {\L}ukasiewicz logic $FD{\L}_n$ with application to Digital Forensics‎. Manuscript profile
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  5 - ‎On The Spectrum of Countable MV-algebras
  Giacomo Lenzi
  10.30495/tfss.2023.1991906.1082
  In this paper we consider MV-algebras and their prime spectrum. We show that there is an uncountable MV-algebra that has the same spectrum as the free MV-algebra over one element, that is, the MV-algebra F ree1 of McNaughton functions from [0, 1] to [0, 1], the continuo More

  In this paper we consider MV-algebras and their prime spectrum. We show that there is an uncountable MV-algebra that has the same spectrum as the free MV-algebra over one element, that is, the MV-algebra F ree1 of McNaughton functions from [0, 1] to [0, 1], the continuous, piecewise linear functions with integer coefficients. The construction is heavily based on Mundici equivalence between MV-algebras and lattice ordered abelian groups with the strong unit. Also, we heavily use the fact that two MV-algebras have the same spectrum if and only if their lattice of principal ideals is isomorphic. As an intermediate step we consider the MV-algebra A1 of continuous, piecewise linear functions with rational coefficients. It is known that A1 contains F ree1, and that A1 and F ree1 are equispectral. However, A1 is in some sense easy to work with than F ree1. Now, A1 is still countable. To build an equispectral uncountable MV-algebra A2, we consider certain “almost rational” functions on [0, 1], which are rational in every initial segment of [0, 1], but which can have an irrational limit in 1. We exploit heavily, via Mundici equivalence, the properties of divisible lattice ordered abelian groups, which have an additional structure of vector spaces over the rational field. Manuscript profile