On implicative and maximal ideals of BL-algebras

Andrzej Walendziak. "On implicative and maximal ideals of BL-algebras." Commentationes Mathematicae 54.2 (2014): null. <http://eudml.org/doc/292553>.

@article{AndrzejWalendziak2014,
abstract = {In the theory of MV-algebras, implicative ideals are studied by Hoo and Sessa. In this paper we define and characterize implicative ideals of BL-algebras. We also investigate maximal ideals of BL-algebras and prove that if an ideal is prime and implicative, then it is maximal. Moreover, we show that an ideal is maximal if and only if the quotient BL-algebra is a simple MV-algebra. Finally, we give the homomorphic properties of implicative and maximal ideals.},
author = {Andrzej Walendziak},
journal = {Commentationes Mathematicae},
keywords = {BL-algebra, MV-algebra, implicative (maximal) ideal},
language = {eng},
number = {2},
pages = {null},
title = {On implicative and maximal ideals of BL-algebras},
url = {http://eudml.org/doc/292553},
volume = {54},
year = {2014},
}

TY - JOUR
AU - Andrzej Walendziak
TI - On implicative and maximal ideals of BL-algebras
JO - Commentationes Mathematicae
PY - 2014
VL - 54
IS - 2
SP - null
AB - In the theory of MV-algebras, implicative ideals are studied by Hoo and Sessa. In this paper we define and characterize implicative ideals of BL-algebras. We also investigate maximal ideals of BL-algebras and prove that if an ideal is prime and implicative, then it is maximal. Moreover, we show that an ideal is maximal if and only if the quotient BL-algebra is a simple MV-algebra. Finally, we give the homomorphic properties of implicative and maximal ideals.
LA - eng
KW - BL-algebra, MV-algebra, implicative (maximal) ideal
UR - http://eudml.org/doc/292553
ER -