μ-半环和弱归纳~＊-半环

On μ-semirings and weak inductive~＊-semirings

目的研究了μ-半环和弱归纳*-半环的上(下)三角矩阵的全体所形成的半环。方法采用了归纳的方法。结果得到了μ-半环的上(下)三角矩阵的全体所形成的半环仍然是μ-半环,以及弱归纳*-半环的上(下)三角矩阵的全体所形成的半环仍然是弱归纳*-半环。结论μ-半环和弱归纳*-半环的矩阵理论也可以运用到计算机科学中。

Aim The paper studys the semiring of all upper（lower） triangular matrices on a μ-semiring and a weak inductive＊-semiring.Methods The method of induction is used.Results The semiring of all upper（lower） triangular matrices on a μ-semiring is also a μ-semiring,and the semiring of all upper（lower） triangular matrices on a weak inductive＊-semiring is also a weak inductive＊-semiring.Conclusion The matrice theory of μ-semirirgs and weak inductive ＊-semirings can also be used in the computer science.