相关论文: On the Koszul Betti numbers in positive characteri…

This paper has been withdrawn by the author due to a crucial mistakes.

This paper has been withdrawn by the author due to a crucial error.

This paper has been withdrawn by the author due to an error in the data-analysis.

The paper has been withdrawn.

This paper has been withdrawn by the author for further investigation.

This paper has been withdrawn by the author [arXiv admin].

This paper has been withdrawn by the author due to rewritting and skipping crucial sign errors.

This paper has been withdrawn by the author due to a crucial sign error in equation 1.

This article is withdrawn because of a mistake in the main result of the paper.

This paper has been withdrawn by the authors, due a crucial error.

This paper has been withdrawn due to a missing hypothesis in the main statement.

This paper is withdrawn. The current main theorem can be proved by using a simple field theory. The main theorem is to placed by another theorem, shortly.

This paper has been withdrawn by the authors due to a mistake in the proof of the chief result. In particular Theorem 1.3 is correct, while Theorem 1.1 and Theorem 1.2 hold with \mu>0 and a suitable restriction on the exponent p. The proof…

Let $G$ be a finitely generated right $A$-module for a finite-dimensional algebra $A$ over a filed $\Bbbk$, and $\mathcal{I}$ the additive closure of $G$. We will define a $\mathcal{I}$-relative Koszul coresolution…

Paper has been withdrawn for major repairs.

We withdraw our paper for one doubt on one of equations .Due to this reason we will check again our calculation and replace the revised version of this paper.

This paper represents the main portion of the Ph.D. Thesis of the author, and is the first of the series of four papers, which is a joint work with K. Matsuki as a whole. We present a program toward constructing an algorithm for resolution…

This paper has been withdrawn by the authors, due an error in Bethe Ansatz equations (16).

This paper has been withdrawn by the authors due to substantial changes.

The paper has been withdrawn by the authors