Completely Prime Modules Over Path Algebras for Dynkin Quiver of Type A_n and D_n

DOI

10.2991/assehr.k.210508.037How to use a DOI?

Keywords

Completely Prime Module, Path Algebra, Dynkin

Abstract

Let K be a field and Q be a quiver (directed graph), and let A = KQ be the path algebra that corresponds to Q with coefficients in K. An A-module M is a completely prime (c-prime) module in the sense that rm = 0 for one m ∈ M and r ∈ A implies that either r annihilates all M or m = 0. In this paper, we prove that for Dynkin quiver type A_n and D_n, an A-module M is c-prime if and only if it is simple.

Copyright

© 2021, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Risnawita
AU  - Irawati
AU  - I. Muchtadi-Alamsyah
PY  - 2021
DA  - 2021/05/11
TI  - Completely Prime Modules Over Path Algebras for Dynkin Quiver of Type An and Dn
BT  - Proceedings of the 1st International Conference on Mathematics and Mathematics Education (ICMMEd 2020)
PB  - Atlantis Press
SP  - 23
EP  - 28
SN  - 2352-5398
UR  - https://doi.org/10.2991/assehr.k.210508.037
DO  - 10.2991/assehr.k.210508.037
ID  - 2021
ER  -