Quasi-subtractive varieties: open filters, congruences, and the commutator

Quasi-subtractive varieties are a generalization of subtractive varieties, introduced to account for some correspondence theorems between ideals and congruences in the literature that are not corollaries of general theorems in the theory of subtractive varieties. The main tool for the investigation of quasi-subtractive varieties is the concept of open filter, that extends the notion of ideal due to Gumm and Ursini. In this paper, we explore further the fundamental properties of open filters and congruences in this context; moreover, we introduce and investigate a notion of commutator of open filters.