Related papers: Hereditary is Hereditary

This paper has been withdrawn by the author due a crucial error.

This paper has been withdrawn.

The paper has been withdrawn due to very low reproducibility. About 100 samples have been made, only 3 samples show the superconducting-like behavior. We think it may be an unlikely result.

This paper has been withdrawn by the authors, because of a crucial gap in the proof of the main theorem.

This paper has been withdrawn by the author due to a the manuscript error.

The paper is withdrawn. The proof has an error and it requires a different approach.

In this short paper we prove that a finite dimensional algebra is hereditary if and only if there is no loop in its ordinary quiver and every $\tau$-tilting module is tilting.

The paper has been withdrawn by the authors

This paper has been withdrawn by the authors, because of serious experimental problems.

This paper has been withdrawn by the author, due a crucial mistake in proof of lemma 4.2.

This paper has been withdrawn by the authors due to a crucial error.

This paper has been withdrawn by the authors. Because of a misunderstanding, the paper was submitted prematurely to the arXiv. A replacement will follow.

This paper has been withdrawn. The authors realized that the obtained results were not new.

The paper is being withdrawn. A new submission will follow.

This paper has been withdrawn by the author due to a crucial sign error.

This paper has been withdrawn.

We discuss some recent developments in the theory of abelian model categories. The emphasis is on the hereditary condition and applications to homotopy categories of chain complexes and stable module categories.

This paper has been withdrawn by the authors.

The paper has been withdrawn by the author, due to it being fundamentally flawed. The author apologizes for any inconvenience it may have caused.

This paper has been withdrawn by the author due to new results to be added.