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dc.contributor.authorAmr Ali, Al-Maktry-
dc.date.accessioned2023-04-26T02:40:24Z-
dc.date.available2023-04-26T02:40:24Z-
dc.date.issued2021-
dc.identifier.urihttps://link.springer.com/article/10.1007/s00200-021-00510-x-
dc.identifier.urihttps://dlib.phenikaa-uni.edu.vn/handle/PNK/8312-
dc.descriptionCC BYvi
dc.description.abstractLet R be a finite commutative ring. The set F(R) of polynomial functions on R is a finite commutative ring with pointwise operations. Its group of units F(R)× is just the set of all unit-valued polynomial functions. We investigate polynomial permutations on R[x]/(x2)=R[α], the ring of dual numbers over R, and show that the group PR(R[α]) , consisting of those polynomial permutations of R[α] represented by polynomials in R[x], is embedded in a semidirect product of F(R)× by the group P(R) of polynomial permutations on R. In particular, when R=Fq , we prove that PFq(Fq[α])≅P(Fq)⋉θF(Fq)×. Furthermore, we count unit-valued polynomial functions on the ring of integers modulo pn and obtain canonical representations for these functions.vi
dc.language.isoenvi
dc.publisherSpringervi
dc.subjectF(R)vi
dc.subjectR[x]/(x2)=R[α]vi
dc.titleOn the group of unit-valued polynomial functionsvi
dc.typeBookvi
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