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In this paper, we study the closedness such as seminomality and $t$-closedness, and Noetherian-like properties such as piecewise Noetherianness and Noetherian spectrum, of Hurwitz polynomial rings and Hurwitz series rings. To do so, we construct an isomorphism between a Hurwitz polynomial ring (resp., a Hurwitz series ring) and a factor ring of a polynomial ring (resp., a power series ring) in a countably infinite number of indeterminates.
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참고문헌 (33)
참고문헌 신청
J. A. Beachy / 1984 / Piecewise Noetherian rings / Comm. Algebra 12(21-22):2679~2706
A. Benhissi / 2007 / Ideal structure of Hurwitz series rings / Beitrage Algebra Geom. 48(1):251~256
A. Benhissi / 2014 / Chain condition on annihilators and strongly Hopfian property in Hurwitz series ring / Algebra Colloq. 21(4):635~646
A. Benhissi / 2012 / Basic properties of Hurwitz series rings / Ric. Mat. 61(2):255~273
J. W. Brewer / 1979 / Seminormality and root closure in polynomial rings and algebraic curves / J. Algebra 58(1):217~226
A. Benhissi / 2007 / Ideal structure of Hurwitz series rings / Beitrage Algebra Geom. 48(1):251~256
A. Benhissi / 2014 / Chain condition on annihilators and strongly Hopfian property in Hurwitz series ring / Algebra Colloq. 21(4):635~646
A. Benhissi / 2012 / Basic properties of Hurwitz series rings / Ric. Mat. 61(2):255~273
J. W. Brewer / 1979 / Seminormality and root closure in polynomial rings and algebraic curves / J. Algebra 58(1):217~226
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