Injective Hulls of Semilattices
Injective Hulls of Semilattices
复制标题
DOI：
10.4153/cmb-1970-023-6
复制
发表时间：
1970-03
期刊：
影响因子：
--
通讯作者：
Hulls OF Semilattices;H. Lakser
中科院分区：
文献类型：
--
作者：
Hulls OF Semilattices;H. Lakser
(交)半格是具有一个二元运算∧的代数，它是结合的、交换的和幂等的。在整篇文章中，我们都在研究半格范畴。所有的范畴或一般的代数概念都在这个范畴中被理解。在每个半格S中，这个关系定义了S的一个偏序，符号“∨”表示在这个偏序下的最小上界。如果从偏序集的上下文中不清楚获得最小上界，我们将该集作为索引添加到符号中；例如，∨AX表示偏序集A中X的最小上界。
A (meet-) semilattice is an algebra with one binary operation ∧, which is associative, commutative and idempotent. Throughout this paper we are working in the category of semilattices. All categorical or general algebraic notions are to be understood in this category. In every semilattice S the relation defines a partial ordering of S. The symbol "∨" denotes least upper bounds under this partial ordering. If it is not clear from the context in which partially ordered set a least upper bound is taken, we add this set as an index to the symbol; for example, ∨AX denotes the least upper bound of X in the partially ordered set A.