Quasi relation algebras (qRAs) were first described by Galatos and Jipsen in 2013. They are generalisations of relation algebras and can also be viewed as certain residuated lattice expansions. We identify positive symmetric idempotent elements in qRAs and show that they can be used to construct new qRAs, so-called contractions of the original algebra. We then show that the contraction of a distributive qRA will be representable when the original algebra is representable. Further, we identify a class of distributive qRAs that are not finitely representable.

翻译：拟关系代数（qRA）最初由Galatos和Jipsen于2013年提出。它们是关系代数的推广，也可视为某种剩余格扩张。我们在拟关系代数中识别出正对称幂等元，并证明它们可用于构造新的拟关系代数，即所谓原代数的收缩。随后，我们证明当原代数可表示时，分配拟关系代数的收缩也将是可表示的。此外，我们识别出一类非有限可表示的分配拟关系代数。