| Title: | Monoid algebras and graph products |
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| Authors: | ID Imrich, Wilfried (Author)
ID Klep, Igor (Author)
ID Smertnig, Daniel (Author) |
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| Files: |  PDF - Presentation file, download (443,12 KB)
MD5: B24CC340DB7482219B204BCEDE9BB62C
 URL - Source URL, visit https://adam-journal.eu/index.php/ADAM/article/view/1816
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | 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. |
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| Keywords: | graph products, monoid algebras, power series rings, uniqueness of roots, cancellation property |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.01.2025 |
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| Year of publishing: | 2025 |
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| Number of pages: | 18 str. |
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| Numbering: | Vol. 8, no. 1, article no. P1.11 |
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| PID: | 20.500.12556/DiRROS-22131  |
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| UDC: | 519.17:512 |
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| ISSN on article: | 2590-9770 |
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| DOI: | 10.26493/2590-9770.1816.e85 |
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| COBISS.SI-ID: | 234550019 |
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| Note: |
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| Publication date in DiRROS: | 29.04.2025 |
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| Views: | 576 |
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| Downloads: | 243 |
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| Metadata: |    |
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