Abstract

To study the quotient of algebras, like frames, whose algebraic structures are determined by a partial order, it is often more common to think about sub-kernels of homomorphisms between such algebras. So, in this paper, we first introduce the concept of a pre-congruence on a frame and then characterize them as the sub-kernels of the frame homomorphisms. Second, we characterize the frame congruences as the intersection of a pre-congruence and its inverse. Finally, we prove the decomposition and isomorphism theorems for frame homomorphisms.

中文翻译：

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通过子内核进行帧同余

摘要

为了研究代数的商，如框架，其代数结构由偏序确定，通常更常见的是考虑此类代数之间的同态子核。因此，在本文中，我们首先在框架上引入预同余的概念，然后将它们描述为框架同态的子内核。其次，我们将框架同余描述为预同余及其逆的交集。最后，我们证明了框架同态的分解和同构定理。