Polyadic semigroups and higher regularity
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Abstract
In chapter 3 the regularity concept for semigroups is generalized in two ways simultaneously: to higher regularity and to higher arity. We show that in this approach the one-relational and multi-relational formulations of higher regularity do not coincide, and each element can have several inverses. For polyadic semigroups we introduce several types of higher regularity which satisfy the arity invariance principle: the expressions should not depend of the numerical arity values. We introduce sandwich higher polyadic regularity with generalized idempotents. We use the polyadic-binary correspondence in which the product of a special kind of matrices reproduces the higher regular semigroups and higher braid groups, and the latter are connected with the generalized polyadic braid equation. The higher degree (in our sense) Coxeter group and symmetry groups are then defined.
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persistent_1771691179_6999dcaba715c
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| Authors | Steven Duplij |
| Journal | science and technology of advanced materials |
| Year | 2022 |
| DOI |
10.1088/978-0-7503-2648-3ch3
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| URL | |
| Keywords | Keywords not found |
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