2022/03/29 by Chajda, Ivan, Länger, Helmut
#08A30 #08A40 #08B05 #08B20 #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2203.15871
We study algebras and varieties where every non-trivial congruence has some class being a non-trivial subuniverse of the algebra in question. Then we focus on algebras where this non-trivial class is a unique non-singleton class of the congruence. In particular, we investigate Rees algebras, quasi-Rees algebras and algebras having the one-block-property. We also present results concerning these properties on quotient algebras. Several examples of such algebras and varieties are included.