TY - JOUR
T1 - Von Neumann regularity of smash products associated with G-set gradings
AU - Daua, Leonard
AU - Nastasescu, Constantin
AU - Nastasescu, Maria Monica
PY - 2011/4/1
Y1 - 2011/4/1
N2 - For a G-graded ring R, the problem of Gr-regularity (i.e. von Neumann regularity condition on homogeneous elements) has been treated earlier (see Nǎstǎsescu and Van Oystaeyen, 1982 [11]). Once the concept of the smash product was introduced, this problem has been resumed by several authors. This paper is concerned with von Neumann regularity of two smash products: the smash product R#G of the G-graded ring R by the group G and the smash product R#A of R by a finite left G-set A. The connections between the regularity of R#A and the (Gr-)regularity of R are also investigated. One consequence of our results is that the smash product R#A is a von Neumann regular ring if and only if the category (G,A,R)- gr is regular, in Stenström's sense.
AB - For a G-graded ring R, the problem of Gr-regularity (i.e. von Neumann regularity condition on homogeneous elements) has been treated earlier (see Nǎstǎsescu and Van Oystaeyen, 1982 [11]). Once the concept of the smash product was introduced, this problem has been resumed by several authors. This paper is concerned with von Neumann regularity of two smash products: the smash product R#G of the G-graded ring R by the group G and the smash product R#A of R by a finite left G-set A. The connections between the regularity of R#A and the (Gr-)regularity of R are also investigated. One consequence of our results is that the smash product R#A is a von Neumann regular ring if and only if the category (G,A,R)- gr is regular, in Stenström's sense.
KW - Graded ring
KW - Smash product
KW - Von Neumann regular ring
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U2 - 10.1016/j.jalgebra.2010.11.023
DO - 10.1016/j.jalgebra.2010.11.023
M3 - Article
AN - SCOPUS:79952002494
SN - 0021-8693
VL - 331
SP - 46
EP - 57
JO - Journal of Algebra
JF - Journal of Algebra
IS - 1
ER -