Smarandache戒指
Smarandache Rings
摘要：
通常，在任何人类领域中，集合A上的Smarandache结构意味着A上的弱结构W，使得存在嵌入有更强结构S的真子集B。通过真子集，我们可以理解包含在A中的集合，它不同于空集，不同于单位元素（如果有的话），也不同于A。这些类型的结构发生在我们的日常生活中，这就是为什么我们在这本书中研究它们。因此，作为两种特殊情况：一个Smarandache环的水平I（S-环I）是一个环R，其中包含一个真子集，这是一个域的操作诱导。第二层的Smarandache环（S-环II）是一个环R，它包含一个真子集A，证明：A是一个加法阿贝尔群; A是一个乘法半群，对于a，b属于A，a。b = 0当且仅当a = 0或b = 0。
英文摘要：
Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B which is embedded with a stronger structure S. By proper subset one understands a set included in A, different from the empty set, from the unit element if any, and from A. These types of structures occur in our everyday's life thats why we study them in this book. Thus, as two particular cases: A Smarandache Ring of level I (S-ring I) is a ring R that contains a proper subset that is a field with respect to the operations induced. A Smarandache Ring of level II (S-ring II) is a ring R that contains a proper subset A that verifies: A is an additive abelian group; A is a semigroup under multiplication, for a, b belonging to A, a . b = 0 if and only if a = 0 or b = 0.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
