Radical of ideals in BL-algebras
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In this paper, we introduce the notion of the radical of ideals in $BL$-algebras. With respect to concept, we characterize the notion of the radical of ideals by elements of a $BL$-algebra. Moreover, we prove that in $MV$-algebras, the notion of radical ideals are coincide with the notion of radical ideals in $BL$-algebras. Also, we define the notion of semi maximal ideal in $BL$-algebras and we state and prove some theorems which determine the relationship between this notion and semi maximal filters of a $BL$-algebra. Finally, we prove that ideal $I$ is a semi maximal ideal of $BL$-algebra $L$ \iff $\frac{L}{I}$ is a semisimple ($MV$)$BL$-algebra.
Abstract
In this paper, we introduce the notion of the radical of ideals in $BL$-algebras. With respect to concept, we characterize the notion of the radical of ideals by elements of a $BL$-algebra. Moreover, we prove that in $MV$-algebras, the notion of radical ideals are coincide with the notion of radical ideals in $BL$-algebras. Also, we define the notion of semi maximal ideal in $BL$-algebras and we state and prove some theorems which determine the relationship between this notion and semi maximal filters of a $BL$-algebra. Finally, we prove that ideal $I$ is a semi maximal ideal of $BL$-algebra $L$ \iff $\frac{L}{I}$ is a semisimple ($MV$)$BL$-algebra.
참고문헌 (10)
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