$\mathbb{Z}_2$-graded codimensions of unital algebras

Repovš, Dušan (avtor), Zaicev, Mikhail (avtor)

We study polynomial identities of nonassociative algebras constructed by using infinite binary words and their combinatorial properties. Infinite periodic and Sturmian words were first applied for constructing examples of algebras with an arbitrary real PI-exponent greater than one. Later, we used these algebras for a confirmation of the conjecture that PI-exponent increases precisely by one after adjoining an external unit to a given algebra. Here, we prove the same result for these algebras for graded identities and graded PI-exponent, provided that the grading group is cyclic of order two.

• Jezik: Angleški jezik
• Ključne besede: polynomial identities, graded algebras, codimensions, exponential growth
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: PEF - Pedagoška fakulteta; FMF - Fakulteta za matematiko in fiziko
• Leto izida: 2018
• Št. strani: Str. 483-500
• Številčenje: Vol. 28, no. 3
• PID: 20.500.12556/RUL-109453
• UDK: 512.554
• ISSN pri članku: 0218-1967
• DOI: 10.1142/S0218196718500224
• COBISS.SI-ID: 18344281
• Datum objave v RUL: 03.09.2019

REPOVŠ, Dušan in ZAICEV, Mikhail, 2018, ▫$\mathbb{Z}_2$▫-graded codimensions of unital algebras. International journal of algebra and computation [na spletu]. 2018. Vol. 28, no. 3, p. 483–500. [Dostopano 8 april 2025]. DOI 10.1142/S0218196718500224. Pridobljeno s: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=slv&id=109453

Gradivo je del revije

• Naslov: International journal of algebra and computation
• Skrajšan naslov: Int. j. algebra comput.
• Založnik: World Scientific
• ISSN: 0218-1967
• COBISS.SI-ID: 1554709