THE FIRST U-EXTENSION MODULE AS CLASSES OF SHORT U-EXACT SEQUENCES

Authors

  • Yudi Mahatma Program Studi S1 Matematika, Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Negeri Jakarta, Jalan Rawamangun Muka, Jakarta, 13220, Indonesia.

DOI:

https://doi.org/10.25077/jmu.10.4.553-560.2021

Abstract

Inspired by the notions of the U-exact sequence introduced by Davvaz and Parnian-Garamaleky in 1999, and of the chain U-complex introduced by Davvaz and Shabani-Solt in 2002, Mahatma and Muchtadi-Alamsyah in 2017 developed the concept of the U-projective resolution and the U-extension module, which are the generalizations of the concept of the projective resolution and the concept of extension module, respectively. It is already known that every element of a first extension module can be identified as a short exact sequence. To the simple, there is a relation between the first extension module and the short exact sequence. It is proper to expect the relation to be provided in the U-version. In this paper, we aim to construct a one-one correspondence between the first U-extension module and the set consisting of equivalence classes of short U-exact sequence.

Keywords: Chain U-complex, U-projective resolution, U-extension module

Author Biography

Yudi Mahatma, Program Studi S1 Matematika, Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Negeri Jakarta, Jalan Rawamangun Muka, Jakarta, 13220, Indonesia.

Program Studi S1 Matematika, Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Negeri Jakarta, Jalan Rawamangun Muka, Jakarta, 13220, Indonesia.

References

Davvaz, B., Shabani-Solt, H., 2002, A generalization of homological algebra, J. Korean Math. Soc. No. 6, 39 : 891 – 898

Davvaz, B., Parnian-Garamaleky, A., 1999, A note on exact sequences, Bull. Malaysian Math. Soc. (Second Series), 22 : 53 – 56

Mahatma, Y., Muchtadi-Alamsyah, I., 2017, Construction of U-extension module, AIP Conference Proceedings, 1867 : 020025-1 – 020025-9

Rotman, J. J., 2009, Introduction to Homological Algebra, Edisi ke-2, Springer, New York.

Baur, K., Mahatma, Y., Muchtadi-Alamsyah, I., 2019, The U-projective resolution of modules over path algebras of type An and An, Communications of the Korean Mathematical Society, 34 : 701 – 718

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Published

21-10-2021

Issue

Vol. 10 No. 4 (2021)

Section

Articles

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