20.500.12556/RUP-21971 Monoid algebras and graph products Monoidne algebre in grafovski produkti In this note, we extend results about unique n^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 grafovski produkti monoidne algebre kolobarji potenčnih vrst enkratnost korenov izbris true false true Založba Univerze na Primorskem Angleški jezik Slovenski jezik Neznano 2025-10-21 10:06:07 2025-10-21 10:06:07 2025-11-11 03:03:36 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 2025-04-22 519.17 2590-9770 10.26493/2590-9770.1816.e85 234550019 ADAM_Imrich,_Klep,Smertnig_2025.pdf ADAM_Imrich,_Klep,Smertnig_2025.pdf 1 B6924DDEC5F50E806B534E2B7BFA1784 085abc9130a29b571ee4337694edf8851608016e719c41b1addf792ecd569e9a 029a1cf1-ae56-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=31904 Založba Univerze na Primorskem 0 0 0