Nonfinitely based ai-semirings with finitely based semigroup reducts

Nonfinitely Based Tropical Semirings

On Finitely Based Groups and Nonfinitely Based Quasivarieties

We define the notion of strictly finitely based varieties of groups, and determine which finite groups are strictly finitely based. Then we use this result to prove the existence of ‘very nonfinitely based’ finite algebras, thereby solving two open problems in the theory of quasivarieties.

Syntactic semigroup problem for the semigroup reducts of Affine Near-semirings over Brandt Semigroups

The syntactic semigroup problem is to decide whether a given finite semigroup is syntactic or not. This work investigates the syntactic semigroup problem for both the semigroup reducts of A(Bn), the affine nearsemiring over a Brandt semigroup Bn. It is ascertained that both the semigroup reducts of A(Bn) are syntactic semigroups.

A minimal nonfinitely based semigroup whose variety is polynomially recognizable

We exhibit a 6-element semigroup that has no finite identity basis but nevertheless generates a variety whose finite membership problem admits a polynomial algorithm. 1 Motivation and overview Developments in the theory of computational complexity have shed new light on algorithmic aspects of algebra. It has turned out that many basic algo-rithmic questions whose decidability is well known and/...

A New Example of a Minimal Nonfinitely Based Semigroup

Only three of the 15 973 distinct six-element semigroups are presently known to be nonfinitely based. This paper introduces a fourth example. 2010 Mathematics subject classification: primary 20M07.