The purpose of this paper is to study the commutative pseudomeadows, the structure which is defined in the same way as commutative meadows, except that the existence of a multiplicative identity is not required. We extend the characterization of finite commutative meadows, given by I. Bethke, P. Rodenburg, and A. Sevenster in their paper (2015), to the case of commutative pseudomeadows with finitely many idempotents. We also extend the well-known characterization of general commutative meadows as...

Let τ: F → N be a type of algebras, where F is a set of fundamental operation symbols and N is the set of all positive integers. An identity φ ≈ ψ is called biregular if it has the same variables in each of it sides and it has the same fundamental operation symbols in each of it sides. For a variety V of type τ we denote by $V_b$ the biregularization of V, i.e. the variety of type τ defined by all biregular identities from Id(V). Let B be the variety of Boolean algebras of type ${\tau }_b:+,·,´\to N$, where ${\tau }_b(+)={\tau }_b\left(·\right)=2$ and ${\tau }_b\left(´\right)=1$. In...