- Tytuł:
- Weak Baer modules over graded rings
- Autorzy:
-
Teply, Mark
Torrecillas, Blas - Powiązania:
- https://bibliotekanauki.pl/articles/965999.pdf
- Data publikacji:
- 1998
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Opis:
- In [2], Fuchs and Viljoen introduced and classified the $B^*$-modules for a valuation ring R: an R-module M is a $B^*$-module if $Ext^1_R(M,X)=0$ for each divisible module X and each torsion module X with bounded order. The concept of a $B^*$-module was extended to the setting of a torsion theory over an associative ring in [14]. In the present paper, we use categorical methods to investigate the $B^*$-modules for a group graded ring. Our most complete result (Theorem 4.10) characterizes $B^*$-modules for a strongly graded ring R over a finite group G with $|G|^{−1} \in R$. Motivated by the results of [8], [9], [10] and [15], we also study the condition that every non-singular R-module is a $B^∗$-module with respect to the Goldie torsion theory; for the case in which R is a strongly graded ring over a group, extensive information is obtained for group rings of abelian, solvable and polycyclic-by-finite groups.
- Źródło:
-
Colloquium Mathematicum; 1998, 75, 1; 19-31
0010-1354 - Pojawia się w:
- Colloquium Mathematicum
- Dostawca treści:
- Biblioteka Nauki
Artykuł