TY - JOUR ID - 130076 TI - Primeness of simple modules over path algebras and Leavitt path algebras JO - Khayyam Journal of Mathematics JA - KJM LA - en SN - AU - Risnawita, Risnawita AU - Irawati, Irawati AU - Alamsyah, Intan Muchtadi AD - Institut Teknologi Bandung AD - Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung 40132, Indonesia. Y1 - 2021 PY - 2021 VL - 7 IS - 2 SP - 219 EP - 231 KW - Prime Modules KW - Path Algebras KW - Leavitt Path Algebras DO - 10.22034/kjm.2021.203331.1578 N2 - Let K be a field and E be a directed graph, called quiver in thefollowing, and let A = KE be the path algebra that corresponds to E withcoefficients in K. An A-module M is a c-prime module in the sense that rm = 0for one m in M and r in A implies that either r annihilates all M or m = 0. Inthis paper, we prove that for any acyclic graph E, an A-module M is c-primeif and only if it is simple. The primeness of simple modules over Leavitt pathalgebras is also discussed. We prove that some classes of simple modules overLeavitt path algebras, are not c-prime modules. UR - https://www.kjm-math.org/article_130076.html L1 - https://www.kjm-math.org/article_130076_103bbc02d81ad766f14dd138a47f29a8.pdf ER -