We present some general results implying nonfinite axiomatisability of many additively
idempotent semirings with finitely based semigroup reducts. The smallest is a 3-element …

Restriction semigroups model algebras of partial maps under composition and domain.
Here we consider restriction semigroups for which the usual Boolean operations on …

Abstract We study the Finite Basis Problem for finite additively idempotent semirings whose
multiplicative reducts are inverse semigroups. In particular, we show that each additively …

We give complete, finite quasiequational axiomatisations for algebras of unary partial
functions under the operations of composition, domain, antidomain, range and intersection …

The" if–then–else" construction is one of the most elementary programming commands, and
its abstract laws have been widely studied, starting with McCarthy. Possibly, the most …

The semigroup of all partial maps on a set under the operation of composition admits a
number of operations relating to the domain and range of a partial map. Of particular interest …

We describe which subdirectly irreducible flat algebras arise in the variety generated by an
arbitrary class of flat algebras with absorbing bottom element. This is used to give an …

A recent study of the override and update operations defined on sets of partial functions
placed both operations within the algebraic context of a certain variety of algebras. We show …

The equational complexity function growth among varieties of semilattice-ordered inverse
semigroups and additive idempotent semirings. We also examine a quasivariety analogue …