论文标题
代数的共同体和Cosmash产品
Associativity and the cosmash product in operadic varieties of algebras
论文作者
论文摘要
在本文中，我们通过（分类）条件：所谓的cosmash产品的关联性来表征田地上的多种交往代数。与换向者理论密切相关的这种情况非常强烈：例如，群体不满足。然而，在交流代数的情况下，Cosmash产品不过是张量产品。这解释了为什么在这种情况下是关联的原因。我们证明，在代数在一个字段上的运营品种的设置中，这是唯一的例子。还讨论了非自动案例中的进一步示例。
In this article, we characterise the operadic variety of commutative associative algebras over a field via a (categorical) condition: the associativity of the so-called cosmash product. This condition, which is closely related to commutator theory, is quite strong: for example, groups do not satisfy it. However, in the case of commutative associative algebras, the cosmash product is nothing more than the tensor product; which explains why in this case it is associative. We prove that in the setting of operadic varieties of algebras over a field, it is the only example. Further examples in the non-operadic case are also discussed.
