Computational Complexity of Some Problems Involving Congruences on Algebras

We prove that several problems concerning congruences on algebras are complete for nondeterministic log-space. These problems are: determining the congruence on a given algebra generated by a set of pairs, and determining whether a given algebra is simple or subdirectly irreducible. We also consider the problem of determining the smallest fully invariant congruence on a given algebra containing a given set of pairs. We prove that this problem is complete for nondeterministic polynomial time. Key words and phrases. congruence, simple algebra, nondeterministic log-space, graph accessibility One of the fundamental constructions in algebra is the formation of quotient structures. Every quotient of an algebra A is a homomorphic image of A, and conversely, every homomorphic image is isomorphic to a quotient of A. For familiar sorts of algebraic structures such as groups or rings, a quotient is often determined by a special subset, i.e., a normal subgroup or an ideal. But for an arbitrary alg...

• Type: Conference
• Year: 2000
• Where: LICS
• Authors: Clifford Bergman, Giora Slutzki
• Keywords: Algebra, Automated Reasoning, LICS 2000, Nondeterministic Log-space, Quotient