Extensions of iterative congruences on free iterative algebras

摘要

This paper investigates special congruences on RΣ (the Σ-algebra of partial regular trees) which extend congruences on RΣ (the Σ-algebra of total regular trees). It is proved that if a congruence on RΣ induces an iterative factor algebra, then so does its extension on RΣ. This result is used to show that if an iterative algebra admits a faithful regular extension, then that extension, then that extension is again iterative.