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A property of the complex semigroup algebra of a free monoid. (English) Zbl 1104.16021
Summary: It is shown that the complex semigroup algebra of a free monoid of rank at least two is *-primitive, where * denotes the involution on the algebra induced by word-reversal on the monoid.

16S36 Ordinary and skew polynomial rings and semigroup rings
20M25 Semigroup rings, multiplicative semigroups of rings
16D60 Simple and semisimple modules, primitive rings and ideals in associative algebras
20M05 Free semigroups, generators and relations, word problems
Full Text: DOI
[1] DOI: 10.1112/blms/8.2.156 · Zbl 0328.43011 · doi:10.1112/blms/8.2.156
[2] DOI: 10.1112/blms/8.3.294 · Zbl 0344.20002 · doi:10.1112/blms/8.3.294
[3] DOI: 10.1016/0022-1236(80)90010-5 · Zbl 0465.46051 · doi:10.1016/0022-1236(80)90010-5
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[6] DOI: 10.1017/S0013091500020526 · Zbl 0948.22009 · doi:10.1017/S0013091500020526
[7] DOI: 10.1007/BF02676603 · Zbl 0870.16018 · doi:10.1007/BF02676603
[8] DOI: 10.1016/0021-8693(73)90011-2 · Zbl 0266.16008 · doi:10.1016/0021-8693(73)90011-2
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