Zur Theorie der Polynomringe |
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Authors: | Prof Dr Wilfried Nöbauer |
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Institution: | 1. IV. Institut für Mathematik, Technische Hochschule, Argentinierstra?e 8, A-1040, Wien, ?sterreich
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Abstract: | Let \(\mathfrak{B}\) be a variety of rings,R a ring of \(\mathfrak{B}\) andx an indeterminate. The free compositionR(x, \(\mathfrak{B}\) ) ofR and the free algebra of \(\mathfrak{B}\) generated byx, is called the \(\mathfrak{B}\) -polynomial ring inx the variety of rings, rings with identity, commutative rings or commutative rings with identity resp. We prove some results about relations between the polynomial ringsR(x, \(\mathfrak{B}\) ), whereR is fixed and \(\mathfrak{B}\) runs over these varieties. Moreover we construct normal form systems for certain polynomial ringsR(x, \(\mathfrak{B}\) ). |
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