21 citations · 23 across the 10 of their papers we have counts for
11 papers
Three Results Concerning Auslander Algebras
Stephen Zito
Our first result provides a new characterization of Auslander algebras using a property of hereditary torsion pairs. The second result shows an Auslander algebra is left or rig…
Several Results Concerning Convex Subcategories
Stephen Zito
We apply the notion of a full convex subcategory to a wide range of algebras including tilted, quasi-tilted, shod, weakly shod, left and right glued, laura, simply connected, stron…
-Tilting Finite Algebras With Nonempty Left Or Right Parts Are Representation-Finite
Stephen Zito
Let be a finite dimensional algebra such that or . Then is -tilting finite if and only if is representation-finite.
1-Auslander-Gorenstein algebras which are tilted
Stephen Zito
Let be a 1-Auslander-Gorenstein Algebra. We give a necessary and sufficient condition for to be a tilted algebra.
-Tilting Finite Cluster-Tilted Algebras
Stephen Zito
Let B be a cluster-tilted algebra. We prove that B is -tilting finite if and only if B is representation-finite.
A New Proof Concerning Quasi-Tilted Algebras
Stephen Zito
Let be a quasi-tilted algebra. If is representation-finite, it was shown by Happel, Reiten, and Smalø that is tilted. We provide a new, short proof of this result.
Auslander algebras which are tilted
Stephen Zito
Let be an Auslander algebra of global dimension equal to 2. We provide a necessary and sufficient condition for to be a tilted algebra. In particular, is tilted if and…
Short Proof of a Conjecture Concerning Split-By-Nilpotent Extensions
Stephen Zito
Let C be a finite dimensional algebra with B a split extension by a nilpotent bimodule E. We provide a short proof to a conjecture by Assem and Zacharia concerning properties of mo…
Bongartz -Complements Over Split-By-Nilpotent Extensions
Stephen Zito
Let C be a finite dimensional algebra with B a split extension by a nilpotent bimodule E, and let M be a -rigid C-module with U its Bongartz -complement. If the induced modul…
Projective Dimensions and Extensions of Modules from Titled to Cluster-Tilted Algebras
Stephen Zito
We study the module categories of a tilted algebra C and the corresponding cluster-tilted algebra B. We investigate how various properties of a C-module are affected when considere…
-Rigid Modules from Tilted to Cluster-Tilted Algebras
Stephen Zito
We study the module categories of a tilted algebra C and the corresponding cluster-tilted algebra B. In particular, we study which -rigid C-modules are also -rigid B-modules.