JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (2): 105-110.doi: 10.6040/j.issn.1671-9352.0.2022.006

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(n,d)-Injective modules over triangular matirx rings

DAIQING Ang-mao, LU Bo   

  1. College of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, Gansu, China
  • Published:2023-02-12

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Abstract: Let A, B be rings, U a (B,A)-bimodule, n, d non-negative integers, T=(A 0U B)a formal triangular matrix ring, firstly, it is shown that M=(M1M2)φM is an n-presented left T-module if and only if M1 is an n-presented left A-module, Coker φM is an n-presented left B-module and φM:UAM1 → M2 is a monomorphism. Secondly, it is shown that M1 is an (n,d)-injective left A-module and M2 is an(n,d)-injective left B-module whenever M=(M1M2)φM is an(n,d)-injective left T-module.

Key words: triangular matirx ring, n-presented module, (n,d)-injective module

CLC Number: 

  • O154.2
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