Pseudo-BCH Semilattices - Walendziak, Andrzej (Bulletin of the Section of Logic, 2018)
In this paper we study pseudo-BCH algebras which are semilattices or lattices with respect to the natural relations <span style="line-height: 115%; font-family: 'Calibri','sans-serif'; font-size: 11pt; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-font-family: CMR9; mso-fareast-language: EN-US; mso-ansi-language: PL; mso-bidi-language: AR-SA;">≤; we call them pseudo-BCH join-semilattices, pseudo-BCH meet-semilattices and pseudo-BCH lattices, respectively. We prove that the class of all pseudo-BCH join-semilattices is a variety and show that it is weakly regular, arithmetical at 1, and congruence distributive. In addition, we obtain the systems of identities defininig pseudo-BCH meet-semilattices and pseudo-BCH lattices.