In: Mathematica Slovaca, vol. 69, no. 4
Rajab Ali Borzooei - M. Shenavaei - Antonio Di Nola - Omid Zahiri
Rok, strany: 2019, 739 - 752
The paper deals with an algebraic extension of MV-semirings based on the definition of generalized Boolean algebras. We propose a semiring-theoretic approach to EMV-algebras based on the connections between such algebras and idempotent semirings. We introduce a new algebraic structure, not necessarily with a top element, which is called an EMV-semiring and we get some examples and basic properties of EMV-semiring. We show that every EMV-semiring is an EMV-algebra and every\linebreak EMV-semiring contains an MV-semiring and an MV-algebra. Then, we study EMV-semiring as a lattice and prove that any EMV-semiring is a distributive lattice. Moreover, we define an EMV-semiring homomorphism and show that the categories of EMV-semirings and the category of EMV-algebras are isomorphic. We also define the concepts of $GI$-simple and DLO-semiring and prove that every EMV-semiring is a $GI$-simple and a DLO-semi ring. Finally, we propose a representation for EMV-semi rings, which proves that any EMV-semi ring is either an MV-semiring or can be embedded into an MV-semi ring as a maximal ideal.
Borzooei, R., Shenavaei, M., Di Nola, A., Zahiri, O. 2019. On EMV-Semirings. In Mathematica Slovaca, vol. 69, no.4, pp. 739-752. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0265
Borzooei, R., Shenavaei, M., Di Nola, A., Zahiri, O. (2019). On EMV-Semirings. Mathematica Slovaca, 69(4), 739-752. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0265
Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava
Publikované: 19. 7. 2019