Noncommutative infinitary semigroups
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910266659176448 |
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| author | Lipparini, Paolo |
| author_facet | Lipparini, Paolo |
| contents | Various kinds of infinitary operations satisfying forms of associativity have been considered in the literature by various authors, including A. Tarski, C. Karp, J. H. Conway, D. Krob, N. Bedon, and C. Rispal. Applications include the arithmetics of binary relations, quasigroups, and automata theory,
We present a general definition for an infinitary noncommutative partial semigroup; the definition extends and encompasses all the previous notions. In particular, we show that new phenomena occur in the noncommutative case, giving rise to a somewhat richer (and, by the way, more difficult) theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_28413 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Noncommutative infinitary semigroups Lipparini, Paolo Group Theory Rings and Algebras 20M75, 08A65 Various kinds of infinitary operations satisfying forms of associativity have been considered in the literature by various authors, including A. Tarski, C. Karp, J. H. Conway, D. Krob, N. Bedon, and C. Rispal. Applications include the arithmetics of binary relations, quasigroups, and automata theory, We present a general definition for an infinitary noncommutative partial semigroup; the definition extends and encompasses all the previous notions. In particular, we show that new phenomena occur in the noncommutative case, giving rise to a somewhat richer (and, by the way, more difficult) theory. |
| title | Noncommutative infinitary semigroups |
| topic | Group Theory Rings and Algebras 20M75, 08A65 |
| url | https://arxiv.org/abs/2605.28413 |