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Multiary Gradings
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DOI：10.3390/axioms15030197.png)
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Abstract
En 中文
This article develops a comprehensive theory of multiary graded polyadic algebras, extending the classical concept of group-graded algebras to higher-arity structures. We introduce the notion of grading by multiary groups and investigate various compatibility conditions between the arity of algebra operations and grading group operations. Key results include quantization rules connecting arities, classification of graded homomorphisms, the First Isomorphism Theorem for graded polyadic algebras and concrete examples including ternary superalgebras and polynomial algebras over n-ary matrices. The theory reveals fundamentally new phenomena not present in the binary case, such as the existence of higher power gradings and nontrivial constraints on arity compatibility.
Keywords:
grading
graded algebra
arity
polyadic ring
n-ary group
polyadic algebra
querelement