Ideals and congruences of basic algebras
According to [\textit{I. Chajda} et al., Algebra Univers. 60, No. 1, 63--90 (2009; Zbl 1219.06013)], a \textit{basic algebra} is an algebra \((A;\oplus,\neg,0, 1)\) such that {\parindent=6mm \begin{itemize}\item[1.] \(x\oplus 0=x,\) \item[2.] \(\neg \neg x = x,\) \item[3.] \(\neg(\neg x \oplus y)\oplus y = \neg (\neg y \oplus x) \oplus x,\) \item[4.] \(\neg(\neg(\neg(x\oplus y)\oplus y)\oplus z)\oplus (x \oplus z)=1.\) \end{itemize}} Examples of basic algebras are MV-algebras and effect algebras. The main aim of the paper under review is to present an internal characterization of congruence kernels that are ideals of basic algebras, and to find a finite basis of ideal terms. In addition, these bases are used to axiomatize the subvariety generated by linearly ordered basic algebras.
scientific article; zbMATH DE number 6173756