Mathematical Sciences: Problems in Universal Algebra

本文将研究泛代数的三个重要性质：合并性、演绎和同余模簇。对融合性的研究主要围绕两个问题展开。1.确定合并性质加上剩余小是否蕴含同余扩张性质。2.品种融合碱基的特征。关于演绎的计划没有那么具体。一般的问题是试图对那些演绎的品种进行分类。第三条途径是同余模簇中交换子的表示问题。所有这些话题都与代数的基础有关，只有在它们制约了关于代数问题的思维模式的情况下，才有可能应用于代数之外。

Three important properties of universal algebras will be studied: the amalgamation property, deductiveness, and congruence modular varieties. The research on the amalgamation property centers on two problems. 1. Determination if the amalgamation property plus residual smallness implies the congruence extension property. 2. Characterization of the amalgamation bases of the variety. The plans for deductiveness are less specific. The general issue is to attempt to classify those varieties that are deductive. A third avenue to be pursued is the representation problem for the commutator in congruence modular varieties. All of these topics concern the foundations of algebra and are likely to be applied outside of algebra only to the extent that they condition a mode of thought about algebraic questions.