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In mathematics, a quasivariety is a class of algebraic structures generalizing the notion of variety by allowing equational conditions on the axioms defining the class. ==Definition== A ''trivial algebra'' contains just one element. A quasivariety is a class ''K'' of algebras with a specified signature satisfying any of the following equivalent conditions. 1. ''K'' is a pseudoelementary class closed under subalgebras and direct products. 2. ''K'' is the class of all models of a set of quasiidentities, that is, implications of the form , where are terms built up from variables using the operation symbols of the specified signature. 3. ''K'' contains a trivial algebra and is closed under isomorphisms, subalgebras, and reduced products. 4. ''K'' contains a trivial algebra and is closed under isomorphisms, subalgebras, direct products, and ultraproducts. 抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Quasivariety」の詳細全文を読む スポンサード リンク
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