Publication:
Invertible matrices in certain commutative subsemirings of full matrix semirings

0
0

Issued Date

2016

Resource Type

Article

File Type

application/pdf

ISSN

13118080

DOI

10.12732/ijpam.v106i1.14

Other identifier(s)

2-s2.0-84957889383

Rights Holder(s)

มหาวิทยาลัยศรีนครินทรวิโรฒ

Bibliographic Citation

International Journal of Pure and Applied Mathematics. Vol 106, No.1 (2016), p.191-197

Suggested Citation

Sirasuntorn N., Sararnrakskul R.I. Invertible matrices in certain commutative subsemirings of full matrix semirings. International Journal of Pure and Applied Mathematics. Vol 106, No.1 (2016), p.191-197. doi:10.12732/ijpam.v106i1.14 Retrieved from: https://hdl.handle.net/20.500.14740/5776

Title

Invertible matrices in certain commutative subsemirings of full matrix semirings

Author(s)

Sirasuntorn N.
 Sararnrakskul R.I.

Abstract

Then every field is a semifield. For a semifield S, we let Dn(S) denote the set of all A ε Mn (S) of the form (Equation Presented) where Mn (S) is the full n × n matrix semiring over S. Then Dn(S) is a maximal commutative subsemiring of the semiring Mn(S). If S is a field, it is known that A ε Dn(S) is invertible if and only if det A ≠ 0. In this paper, invertible matrices in Dn(S) where S is a semifield which is not a field are characterized. It is shown that if S is a semifield which is not a field, then A ε Dn(S) is an invertible matrix over S if and only if (xi = 0 if and only if yi ≠ 0). © 2016 Academic Publications, Ltd.

View online Resources

Research Projects

Organizational Units

Journal Issue

URI

https://hdl.handle.net/20.500.14740/5776

Collections

Scopus: Year 1983-2021

Endorsement

Review

Supplemented By

Referenced By