zbMATH — the first resource for mathematics

On the algebra of a free monoid. (English) Zbl 0860.20050
Let \(F\) denote a subring of the complex field that contains 1 and is closed under complex conjugation. First, it is shown that, with respect to the involution induced by word-reversal, the algebra over \(F\) of a free monoid admits a trace and a separating family of star matrix representations and is isomorphic to a subdirect product of a family of matrix algebras; meanwhile, the involution induced by word-reversal is special. Secondly, similar results are obtained for the algebra over \(F\) of a free monoid with involution.
Reviewer: Li Fang (Nanjing)

20M25 Semigroup rings, multiplicative semigroups of rings
16S36 Ordinary and skew polynomial rings and semigroup rings
20M05 Free semigroups, generators and relations, word problems
16W10 Rings with involution; Lie, Jordan and other nonassociative structures
Full Text: DOI
[1] Petrich, Inverse semigroups (1984)
[2] Passman, The algebraic theory of group rings (1977) · Zbl 0368.16003
[3] DOI: 10.1016/0022-1236(90)90089-4 · Zbl 0708.46051 · doi:10.1016/0022-1236(90)90089-4
[4] DOI: 10.1016/0022-1236(75)90032-4 · Zbl 0299.46047 · doi:10.1016/0022-1236(75)90032-4
[5] DOI: 10.1017/S0004972700015495 · Zbl 0797.20050 · doi:10.1017/S0004972700015495
[6] Crabb, Proc. Roy. Soc. Edinburgh Sect. A 125 pp 1077– (1995) · Zbl 0839.16022 · doi:10.1017/S0308210500022654
[7] Cohn, Free rings and their relations (1971) · Zbl 0232.16003
[8] DOI: 10.1017/S0004972700014854 · Zbl 0845.20051 · doi:10.1017/S0004972700014854
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.