Amalgamation Property in the subvarieties of Gautama and Almost Gautama algebras

TL;DR

This paper investigates the Amalgamation Property in subvarieties of Almost Gautama algebras, identifying which varieties possess this property and exploring related algebraic properties and applications.

Contribution

It determines exactly which subvarieties of AG have the Amalgamation Property and analyzes several related algebraic properties and their implications.

Findings

Four subvarieties of AG have the AP: Boolean, regular double Stone, regular Kleene Stone, and De Morgan Boolean algebras.

Four subvarieties of AG do not have the AP.

The paper explores applications including transferability, injectives, embedding, bounded obstruction, and model companions.

Abstract

Gautama algebras were introduced recently, as a common generalization of regular double Stone algebras and regular Kleene Stone algebras. Even more recently, Gautama algebras were further generalized to Almost Gautama algebras (AG for short). The main purpose of this paper is to investigate the Amalgamation Property (AP, for short) in the subvarieties of the variety AG. In fact, we show that, of the eight nontrivial subvarieties of AG, only four varieties, namely those of Boolean algebras, of regular double Stone algebras, of regular Kleene Stone algebras and of De Morgan Boolean algebras have the AP and the remaining four do not have the AP. We give several applications of this result; in particular, we examine the following properties for the subvarieties of AG: transferability property (TP), having enough injectives (EI), Embedding Property, Bounded Obstruction Property and having a model companion.