交换半环上半线性空间的同态与子空间
发布时间：2018-08-11 19:17
【摘要】：本文主要讨论交换半环上有限生成的半线性空间的同态问题与半线性子空间.首先引入了半线性空间同态、Ker(φ)的定义,并讨论相关性质,给出了两个半线性空间同构的充要条件,证明了两个半线性空间在同构意义下基的不变性.然后给出了任一有限生成半线性空间是自由半线性空间的充要条件和任一有限生成自由半线性空间不同基的基数的取值范围.最后,给出了在一定条件下任意n维向量组能够扩充成半线性空间的基的充要条件,并在此基础上给出了两个子空间的和为直和的充要条件.
[Abstract]:In this paper, we mainly discuss the homomorphism problem and semilinear subspace of finitely generated semilinear spaces over commutative semirings. Firstly, the definition of homomorphism Ker (蠁) in semilinear space is introduced, and the related properties are discussed. The sufficient and necessary conditions for isomorphism of two semilinear spaces are given, and the invariance of the basis of two semilinear spaces in the sense of isomorphism is proved. Then the sufficient and necessary conditions for any finitely generated semilinear space to be a free semilinear space and the range of values of different cardinals for any finitely generated free semilinear space are given. Finally, the sufficient and necessary conditions for any n-dimensional vector system to be extended to the basis of a semilinear space under certain conditions are given, and a sufficient and necessary condition for the sum of two subspaces to be a direct sum is given.
【学位授予单位】：四川师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O153.3
本文编号：2177983
[Abstract]:In this paper, we mainly discuss the homomorphism problem and semilinear subspace of finitely generated semilinear spaces over commutative semirings. Firstly, the definition of homomorphism Ker (蠁) in semilinear space is introduced, and the related properties are discussed. The sufficient and necessary conditions for isomorphism of two semilinear spaces are given, and the invariance of the basis of two semilinear spaces in the sense of isomorphism is proved. Then the sufficient and necessary conditions for any finitely generated semilinear space to be a free semilinear space and the range of values of different cardinals for any finitely generated free semilinear space are given. Finally, the sufficient and necessary conditions for any n-dimensional vector system to be extended to the basis of a semilinear space under certain conditions are given, and a sufficient and necessary condition for the sum of two subspaces to be a direct sum is given.
【学位授予单位】：四川师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O153.3
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