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Rank and determinant functions for matrices over semirings. (English) Zbl 1181.16042
Young, Nicholas (ed.) et al., Surveys in contemporary mathematics. Cambridge: Cambridge University Press (ISBN 978-0-521-70564-6/pbk). London Mathematical Society Lecture Note Series 347, 1-33 (2008).
The paper is a survey of possible definitions of ranks and determinants for matrices over commutative semirings. Semiring analogues of the Dieudonné and Frobenius theorems on linear transformations preserving matrix invariants are given. For the entire collection see [Zbl 1128.00009].

MSC:
16Y60Semirings
15A15Determinants, permanents, other special matrix functions
15A03Vector spaces, linear dependence, rank
15A45Miscellaneous inequalities involving matrices