20.500.12556/RUL-109453 ▫$\mathbb{Z}_2$▫-graded codimensions of unital algebras 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. polynomial identities graded algebras codimensions exponential growth true false true Angleški jezik Ni določen Članek v reviji 2019-09-03 13:13:32 2019-09-03 13:13:33 2022-08-21 03:42:13 0000-00-00 00:00:00 2018 0 0 Str. 483-500 no. 3 Vol. 28 2018 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512.554 0218-1967 10.1142/S0218196718500224 18344281 1554709 RAZ_Repovs_Dusan_i2018.pdf RAZ_Repovs_Dusan_i2018.pdf 1 438C2BFC0C016340786EBFFAFE3CAF3F 3802d662c0060d23cb6da79988cd406fbab2b4dea97ae48d6d605751fbe3f5e5 dee48d9f-a1b6-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=121023 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0