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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)

##### MSC:
 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
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##### References:
 [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
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