# zbMATH — the first resource for mathematics

A condition implying all rational identities. (Une condition impliquant toutes les identités rationnelles.) (French) Zbl 0881.68071
Summary: We show that the condition saying that $$a^*$$ is the smallest idempotent $$\geq 1+a$$ implies all rational identities.

##### MSC:
 68Q45 Formal languages and automata 16Y60 Semirings 68Q70 Algebraic theory of languages and automata
##### Keywords:
semirings; idempotent; rational identities
Full Text:
##### References:
 [1] 1. M. BOFFA, Une remarque sur les systèmes complets d’identités rationnelles, Informatique théorique et Applications/Theoretical Informatics and Applications, 1990, 24, p. 419-423. Zbl0701.68059 MR1079723 · Zbl 0701.68059 · eudml:92366 [2] 2. J. H. CONWAY, Regular Algebra and Finite Machines, Chapman & Hall, 1971. Zbl0231.94041 · Zbl 0231.94041 [3] 3. D. C. KOZEN, On Kleene Algebras and Closed Semirings, Springer Lecture Notes in Computer Science, 1990, 452, p. 26-47. Zbl0732.03047 MR1084822 · Zbl 0732.03047 [4] 4. D. C. KOZEN, A completeness theorem for Kleene algebras and the algebra of regular events, Proc. 6th Symp. Logic in Computer Science (IEEE), 1991, p. 214-225. [5] 5. D. KROB, Complete Systems of \beta -rational identities, Theoretical Computer Science, 1991, 89, p. 207-343. Zbl0737.68053 MR1133622 · Zbl 0737.68053 · doi:10.1016/0304-3975(91)90395-I
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.