Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-14T06:58:19.791Z Has data issue: false hasContentIssue false

Full Ideals and Ring Groups in Zn[x]

Published online by Cambridge University Press:  20 November 2018

John A. Suvak*
Affiliation:
4 Outerbridge Street, St. John’s, Newfoundland, Canada, AIE 3X5
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

If we add the operation of composition to the polynomial ring R[X], where R is a commutative ring with identity, we get a tri-operational algebra . A full ideal or tri-operational ideal of is the kernel of a tri-operational homomorphism on . This is equivalent [4, pp. 73–74] to the following: A full ideal of is a ring ideal A of R[x] such that f°gA for every fA and g ∈ R[x].

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Carlitz, L., A Note on Permutation Functions over a Finite Field, Duke Math. Journal, 29 (1962), 325332.Google Scholar
2. Dickson, Leonard Eugene, Introduction to the Theory of Numbers, Dover Publications, Inc., New York, 1929.Google Scholar
3. MacLane, Saunders and Birkhoff, Garrett, Algebra, The MacMillan Company, New York, 1967.Google Scholar
4. Mannos, Murray, Ideals in Tri-operational Algebras I, Reports Math. Colloquium, 7 (1946), 7379.Google Scholar
5. Nöbauer, Wilfred, Über Gruppen von Restklassen nach Restpolynomidealen, Sitsber. Akad. Wiss. Wien, Abt. II, 162 (1953), 207233.Google Scholar
6. Nöbauer, Wilfred, Gruppen von Restpolynomidealrestklassen nach Primzahlpotenzen, Monatsh. f. Math., 59 (1955), 194202.Google Scholar
7. Nöbauer, Wilfred, Ûber die Operation des Einsetzen in Polynomringen, Math. Ann., 134 (1958), 248259.Google Scholar
8. Ore, Oystein, Theory of Monomial Groups, Trans. Amer. Math. Soc, 51 (1942), 1564.Google Scholar