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Accurate Elements and Super-Primitive Elements over Rings

✍ Scribed by Nobuharu Onoda; Takasi Sugatani; Ken-ichi Yoshida

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
168 KB
Volume
245
Category
Article
ISSN
0021-8693

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✦ Synopsis

simple algebraic extension of commutative rings with w x w x identity, and let I be the kernel of the R-algebra map R X Βͺ R ␣ sending X to w x ␣ , where R X is the polynomial ring in one indeterminate over R. Then we say that ␣ is accurate over R if I is generated by nonzero polynomials of least degree in I. The main purpose of this paper is to give several conditions for ␣ to be accurate over R. Our results generalize some work of Nagata and Mirbagheri and Ratliff. We also discuss some related topics, including consideration of relations between accurate elements and super-primitive elements.

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