(m,n)-injective and (m,n)-flat functors

Journal of Lanzhou University of Technology ›› 2024, Vol. 50 ›› Issue (2): 142-147.

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(m,n)-injective and (m,n)-flat functors

ZHU Jun, ZHAO Ren-yu

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received:2023-01-13 Online:2024-04-28 Published:2024-04-29

Abstract

Abstract: Let R be an associative ring with identity, m and n be fixed positive integers. The notions of (m,n)-injective functors and (m,n)-flat functors are introduced. Some properties of these two classes of functors are studied and some equivalent characterizations for (m,n)-coherent rings and Von Neumann regular rings are given in terms of (m,n)-injective functors and (m,n)-flat functors.

Key words: (m,n)-injective functor, (m,n)-flat functor, (m,n)-coherent ring, Von Neumann regular ring, (pre)cover, (pre)envelop

CLC Number:

O153.3

ZHU Jun, ZHAO Ren-yu. (m,n)-injective and (m,n)-flat functors[J]. Journal of Lanzhou University of Technology, 2024, 50(2): 142-147.

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(m,n)-injective and (m,n)-flat functors

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