Some change of rings results on (n, m)-SG modules and (n, m)-SG rings

Abstract

Let $n⩾1$ and $k⩾0$ be fixed integers and R be a ring. We show that R is (n, k)-SG with $\mathrm{G}‐\text{gldim}(R)=k$ if and only if $R[x_1,x_2,\dots ,x_m]$ is $(n,k+m)$-SG with $\mathrm{G}‐\text{gldim}(R[x_1,x_2,\dots ,x_m])=k+m.$ We also give an example of a 2-SG-Dedekind domain which is not an SG-Dedekind domain.

Keywords:

• n-SG-projective module
• n-SG-global dimensions
• n-SG-injective modules

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 13G05
• 13D03
• 13D05
• 13F05

Acknowledgement

The authors would like to say thanks to the referee for his (or her) valuable suggestions.

Additional information

Funding

This work was partially supported by the Department of Mathematics of Kyungpook National University and National Natural Science Foundation of China (Grant No. 11671283). The second author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2017R1C1B1008085).