20.500.12556/RUL-168861 Monoid algebras and graph products In this note, we extend results about unique $n^{\rm th}$ roots and cancellation of finite disconnected graphs with respect to the Cartesian, the strong and the direct product, to the rooted hierarchical products, and to a modified lexicographic product. We show that these results also hold for graphs with countably many finite connected components, as long as every connected component appears only finitely often (up to isomorphism). The proofs are via monoid algebras and generalized power series rings. graph products monoid algebras power series rings uniqueness of roots cancellation property true false true Angleški jezik Angleški jezik Članek v reviji 2025-04-29 13:21:23 2025-04-29 13:21:27 2025-04-30 04:00:51 0000-00-00 00:00:00 2025 0 0 18 str. no. 1, article no. P1.11 Vol. 8 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2025-01-01 519.17:512 2590-9770 10.26493/2590-9770.1816.e85 234550019 adam_1816.pdf adam_1816.pdf 1 B6924DDEC5F50E806B534E2B7BFA1784 085abc9130a29b571ee4337694edf8851608016e719c41b1addf792ecd569e9a ee9c2e78-24eb-11f0-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=209928 https://adam-journal.eu/index.php/ADAM/article/view/1816 1 f0eb46ca-24ea-11f0-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=209927 Fakulteta za matematiko in fiziko 0 0 0