(Para) topological pseudo mV-algebras

Subject Areas : Statistics

Nader Kouhestani ¹ , frazaneh rajabi stodeh ² , beheshteh miri ³

1 - Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
2 - Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
3 - Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran

Received: 2021-08-04 Accepted : 2022-03-07 Published : 2022-08-23

Keywords: فیلترتوپولوژی, شبه - MVجبر)پارا( توپولوژیکی, شبه - MVجبر, - PMVشبه نرم,

Abstract :

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.

References:

[1] R.A. Borzooei, Hee sik kim, N. Kouhestani, Constracting (pre) norms in BL­algebras and its action on
topological BL­algebras, journal of Intelligent fuzzy systems 37(2019), 6969­6959.

[2] R. A. Borzooei, G. R. Rezaei, N. Kouhestani, On (semi) Topological BL­algebra, Iranian Journal of Mathematical Sciences and Informatics (1)6, (2011), 59­77.

 

[3] C.C. Chang, Algebraic analysis of many­valued logics, Trans. Am. Math. Soc. 88 (1958), 490­467.

 

[4] A. Dvurecenskij, Pseudo MV­algebras are intervals in l­groups. j.Austral. Math. soc, 72(2002), 445­427.

 

[5] G. Georgescu, A. Iorgulescu , Pseudo MV­algebras, Mult­ valued log ­ 6 (2001), 135­93.

 

[6] N. Kouhestani, R. A. Borzooei, Topological Residuated lattices, Int. j. Industrial mathematics (2017), val(9),
no.3, 195­183.

 

[7] S. Mehrshad, N. Kouhestani, On Pseudo­Valuations on BCK ­algebras, Filomat, (2018), 4332­4319.

 

[8] M. Najafi, G. R. Rezaei, N. Kouhestani, On (para, quasi) Topological MV­algebra, Fuzzy sets and Systems
313(2017), 104­93.

 

[9] F. R. Setudeh, N. Kouhestani, On (semi) Topological BCC­algebras. Apple. Apple. Math. (2017), 161­143.

 

[10] G. Zegorz dymek, A. walendziak. Semisimple archimedean and semilocal pseudo MV­algebras, Scientiae
Mathematicae Japonicae Online,e­2007, 315–324.