Smarandache特殊定代数结构
Smarandache Special Definite Algebraic Structures
摘要：
在这本书中，我们介绍的概念Smarandache特殊明确的代数结构。我们也可以等价地称它们为Smarandache确定的特殊代数结构。这些新的结构被定义为强代数结构中含有一个弱代数结构的真子集。例如，半群在群中的存在性，或半域在域中的存在性，或半环在环中的存在性。值得注意的是，当代数结构具有有限基数时，这些概念不能被定义，即，当代数结构中元素的个数有限时。这本书有四章。第一章是导论。第二章引入了Smarandache特殊定群和Smarandache特殊定域的概念，并得到了一些有趣的性质。第三章介绍并分析了Smarandache定特殊环、向量空间和线性代数的概念。最后一章提出了200多个问题。
英文摘要：
In this book, we introduce the notion of Smarandache special definite algebraic structures. We can also call them equivalently as Smarandache definite special algebraic structures. These new structures are defined as those strong algebraic structures which have in them a proper subset which is a weak algebraic structure. For instance, the existence of a semigroup in a group or a semifield in a field or a semiring in a ring. It is interesting to note that these concepts cannot be defined when the algebraic structure has finite cardinality i.e., when the algebraic structure has finite number of elements in it. This book has four chapters. Chapter one is introductory in nature. In chapter two, the notion of Smarandache special definite groups and Smarandache special definite fields are introduced and several interesting properties are derived. The notion of Smarandache definite special rings, vector spaces and linear algebras are introduced and analyzed in chapter three. The final chapter suggests over 200 problems.
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