On existence of PI-exponents of unital algebras
We construct a family of unital non-associative algebras $ \{T_\alpha\vert\; 2 2 $. This is the first example of a unital algebra whose PI-exponent does not exist.
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| Veröffentlicht in: | Electronic Research Archive 2020-06, Vol.28 (2), p.853-859 |
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| container_title | Electronic Research Archive |
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| creator | Repovš, Dušan D. Zaicev, Mikhail V. |
| description | We construct a family of unital non-associative algebras $ \{T_\alpha\vert\; 2 2 $. This is the first example of a unital algebra whose PI-exponent does not exist. |
| doi_str_mv | 10.3934/era.2020044 |
| format | Article |
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In particular, it follows that ordinary PI-exponent of codimension growth of algebra <inline-formula><tex-math id="M4">$ T_\alpha $</tex-math></inline-formula> does not exist for any <inline-formula><tex-math id="M5">$ \alpha> 2 $</tex-math></inline-formula>. This is the first example of a unital algebra whose PI-exponent does not exist.]]></description><identifier>ISSN: 2688-1594</identifier><identifier>EISSN: 2688-1594</identifier><identifier>DOI: 10.3934/era.2020044</identifier><language>eng</language><publisher>AIMS Press</publisher><subject>Algebra</subject><ispartof>Electronic Research Archive, 2020-06, Vol.28 (2), p.853-859</ispartof><rights>COPYRIGHT 2020 AIMS Press</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c337t-945aad876803a37fd6a92106b3013f39b170da6e4efdc347f28bb2abf99ad04c3</citedby><cites>FETCH-LOGICAL-c337t-945aad876803a37fd6a92106b3013f39b170da6e4efdc347f28bb2abf99ad04c3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27923,27924</link.rule.ids></links><search><creatorcontrib>Repovš, Dušan D.</creatorcontrib><creatorcontrib>Zaicev, Mikhail V.</creatorcontrib><title>On existence of PI-exponents of unital algebras</title><title>Electronic Research Archive</title><description><![CDATA[We construct a family of unital non-associative algebras <inline-formula><tex-math id="M1">$ \{T_\alpha\vert\; 2<\alpha\in\mathbb R\} $</tex-math></inline-formula> such that <inline-formula><tex-math id="M2">$ \underline{exp}(T_\alpha) = 2 $</tex-math></inline-formula>, whereas <inline-formula><tex-math id="M3">$ \alpha\le\overline{exp}(T_\alpha)\le\alpha+1 $</tex-math></inline-formula>. In particular, it follows that ordinary PI-exponent of codimension growth of algebra <inline-formula><tex-math id="M4">$ T_\alpha $</tex-math></inline-formula> does not exist for any <inline-formula><tex-math id="M5">$ \alpha> 2 $</tex-math></inline-formula>. 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In particular, it follows that ordinary PI-exponent of codimension growth of algebra <inline-formula><tex-math id="M4">$ T_\alpha $</tex-math></inline-formula> does not exist for any <inline-formula><tex-math id="M5">$ \alpha> 2 $</tex-math></inline-formula>. This is the first example of a unital algebra whose PI-exponent does not exist.]]></abstract><pub>AIMS Press</pub><doi>10.3934/era.2020044</doi><tpages>7</tpages><oa>free_for_read</oa></addata></record> |
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| subjects | Algebra |
| title | On existence of PI-exponents of unital algebras |
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