n-Star modules over ring extensions

作者：Wei Jiaqun^*

来源：Journal of Algebra, 2007, 310(2): 903-916.

DOI：10.1016/j.jalgebra.2006.10.026

• star modules
• tilting modules
• ring extension

We give conditions under which an n-star module U-A extends to an n-star module, or an n-tilting module, R-R circle times U-A over a ring extension R of A. In case that R is a split extension of A by Q, we obtain that R-R circle times U-A is a 1-tilting module (respectively, a 1-star module) if and only if U-A is a 1-tilting module (respectively, a 1-star module) and U-A generates both (A)Q circle times U-A and AHOM (A)(Q, D) (respectively, U-A generates (A)Q circle times U-A), where D-A is an injective cogenerator in the category of all left A-modules. These extend results in [I. Assem, N. Marmaridis, Tilting modules over split-by-nilpotent extensions, Comm. Algebra 26 (1998) 1547-1555; K.R. Fuller, *-Modules over ring extensions, Comm. Algebra 25 (1997) 2839-2860] by removing the restrictions on R and Q.

• 出版日期2007-4-15
• 单位南京师范大学