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math.RA2026
Transpose Symmetry of Injectivity over Commutative Semirings
Sixuan Gu, Wei Qi, Yaoyu Cheng
Let R be a commutative semiring, not necessarily with a multiplicative identity, and let A be an element of Mn(R). We prove that the map x to Ax on Rn is injective if and only if x…
math.RA2024
A note on pure-semisimple rings
Xiaolei Zhang, Wei Qi
In this note, we give several characterizations of left pure-semisimple in terms of the (pre)envelope, (pre)cover, direct limits, direct sums, inverse limits and direct products pr…