TERM REWRITE RULES FOR FINITE FIELDS
1991 ◽
Vol 01
(03)
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pp. 353-369
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Keyword(s):
Let F1, …, Fk be finite fields with distinct characteristics. We give a finite set of equations which axiomatize the equational theory of F1, …, Fk and then use these axioms to find a finite set of AC-term rewrite rules which is complete for this theory. This gives finite sets of complete AC-term rewrite rules for most instances of xm ≈ x rings by adding new rules to the usual AC-term rewrite rules for commutative rings. The first case for which we do not find a complete set of AC-term rewrite rules is x22 ≈ x, and we doubt that such rules can be found. If R is a set of AC-term rewrite rules from which one can derive x(y + z) → xy + xz, then we show R cannot be complete for x22 ≈ x rings.
1976 ◽
Vol 15
(2)
◽
pp. 245-251
1995 ◽
Vol 52
(2)
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pp. 215-224
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Keyword(s):
2001 ◽
Vol 38
(1-4)
◽
pp. 1-11
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1977 ◽
Vol 17
(1)
◽
pp. 125-134
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Keyword(s):