$K$-radical classes and product radical classes of $MV$-algebras

Year, pages: 2008, 143 - 154

For an $MV$-algebra $\mathcal{A}$ let $J₀(\mathcal{A})$ be the system of all closed ideals of $\mathcal{A}$; this system is partially ordered by the set-theoretical inclusion. A radical class $X$ of $MV$-algebras will be called a $K$-radical class iff, whenever $\mathcal{A}\in X$ and $\mathcal{A}₁$ is an $MV$-algebra with $J₀(\mathcal{A}₁)\cong J₀(\mathcal{A})$, then $\mathcal{A}₁\in X$. An analogous notation for lattice ordered groups was introduced and studied by Conrad. In the present paper we show that there is a one-to-one correspondence between $K$-radical classes of $MV$-algebras and $K$-radical classes of abelian lattice ordered groups. We also prove an analogous result for product radical classes of \mbox{$MV$-algebras}; product radical classes of lattice ordered groups were studied by Ton.

Jakubík, J. 2008. $K$-radical classes and product radical classes of $MV$-algebras. In Mathematica Slovaca, vol. 58, no.2, pp. 143-154. 0139-9918.

Jakubík, J. (2008). $K$-radical classes and product radical classes of $MV$-algebras. Mathematica Slovaca, 58(2), 143-154. 0139-9918.