Some properties of pseudomeadows

Abstract: 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 2015 paper, to the case of commutative pseudomeadows with finitely many idempotents. We also extend the well-known characterization of general commutative meadows as the subdirect products of fields to the case of commutative pseudomeadows. Finally we investigate localizations of commutative pseudomeadows.