Loading...
Please wait, while we are loading the content...
Similar Documents
A Class of Quasitilted Rings That Are Not Tilted
| Content Provider | Semantic Scholar |
|---|---|
| Author | Ium, Colloqu Cum, Mathemat I. |
| Copyright Year | 2005 |
| Abstract | Based on the work of D. Happel, I. Reiten and S. Smalø on quasitilted artin algebras, the first two authors recently introduced the notion of quasitilted rings. Various authors have presented examples of quasitilted artin algebras that are not tilted. Here we present a class of right quasitilted rings that not right tilted, and we show that they satisfy a condition that would force a quasitilted artin algebra to be tilted. Inspired by the papers [9] and [8] on quasitilted artin algebras, in [6] the first two authors began an investigation of the class of rings R, called right quasitilted rings, admitting a split torsion theory (X ,Y) in Mod-R such that R ∈ Y and proj dimY ≤ 1. A quasitilted artin algebra is one admitting such a torsion theory (X0,Y0) in mod-R, and examples of quasitilted artin algebras that are not tilted can be found in [10], for example. In [6] we present an example of a (non-noetherian) right quasitilted ring and state that, together with the third author, we would subsequently show that it is not tilted. Here we shall verify our statement by presenting a rather large class of right quasitilted rings that are not right tilted. Also, recalling that according to [8] a quasitilted artin algebra is tilted if and only if the torsion free class Y0 in mod-R is cogenerated by a (cotilting) module in mod-R, we shall show that in each of our examples the torsion free class Y is cogenerated by a cotilting module. Throughout we use the terminology and notation introduced in [6] and the standard results and terminology of [1], [5] and [11]. 1. A class of quasitilted triangular matrix rings. In the following, let S be a non-semisimple hereditary prime two-sided Goldie ring with twosided maximal quotient ring Q = Q(S), and let |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://www.impan.pl/shop/publication/transaction/download/product/87684 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
