Abstract
IfV is a variety of Ω-groups and ifG∈V then one can study the algebraG V[x] of polynomials overG andx inV. With respect to addition and substitution,G V[x] is a near-ring. Its zero-symmetric part can excellently be used to describe generated ideals. Also, we study maximal left ideals and get a general result on the structure ofG V[V].
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References
Higgins, P. J.: Groups with multiple operators. Proc. London Math. Soc. (3)6, 366–416 (1956).
Lausch, H., Nöbauer, W.: Algebra of polynomials. Amsterdam: North-Holland. 1973.
Pilz, G.: Near-rings. Amsterdam: North-Holland. 1977.
Pilz, G.: Near-rings of compatible functions. Proc. Edinburgh Math. Soc.23, 87–95 (1980).
Pilz, G., So, Y. S.: Near-rings of polynomials and polynomials functions. J. Austral. Math. Soc. (A)29, 61–70 (1980).
So, Y. S.: Polynom-Fastringe. Dissertation, Univ. Linz (Austria), 1978.
So, Y. S.: Near-rings of polynomials over groups. Submitted.
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This study was kindly supported by the Austrian “Fonds zur Förderung der wissenschaftlichen Forschung” (Projekt Nr. 3479).
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Pilz, G., So, YS. Near-rings of polynomials overΩ-groups. Monatshefte für Mathematik 91, 73–76 (1981). https://doi.org/10.1007/BF01306957
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DOI: https://doi.org/10.1007/BF01306957