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Last name: MORA
First name: Ferdinando
It is well-known that each effective associative ring with identity is endowed with a Buchberger Theory, id est a no- tion of Gr oebner bases and related algorithms. This note is a sort of Do-It-Yourself manual for setting a Groebner bases approach to such a ring.
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The second volume of this comprehensive treatise focusses on Buchberger theory and its application to the algorithmic view of commutative algebra. In distinction to other works, the presentation here is based on the intrinsic linear algebra structure of Groebner bases, and thus elementary considerations lead easily to the state-of-the-art in...
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Buchberger Theory provides, for commutative polynomial rings, computational tools allowing to perform ideal theoretical operations. Such techniques are easily adapted to deal similar problems in the non-commutative setting. I give here an elementary primer
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Following the recent survey on Buchberger-Zacharias Theory for monoid rings R[S] over a unitary effective ring R and an effective monoid S, we propose here a presentation of Buchberger-Zacharias Theory and related Gröbner basis computation algorithms for multivariate Ore extensions of rings presented as modules over a principal ideal domain,...
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In 1990 Cooper (Comm., Cont. and Sign. Proc. 281–286, 1990; Electronic Letters 27(22):2090–2091, 1991; Transactions of the Tenth Army Conference on AppliedMathematics and Computing (1992), vol. 93, U.S. Army, pp. 1–11, 1993) suggested to use Gröbner basis computations in order to deduce error locator polynomials of cyclic codes. The aim of this...
We give a survey of results and applications relating to the theory of Gröbner bases of ideals and modules where the coefficient ring is a finite commutative ring. For applications, we specialize to the case of a finite chain ring.We discuss and compare the main algorithms that may be implemented to compute Gröbner and (in the case of a chain...
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