On local finiteness in the sense of Shirshov

DOI10.1007/BF02218639zbMath0289.17001OpenAlexW2050748197WikidataQ112879243 ScholiaQ112879243MaRDI QIDQ1846925

K. A. Zhevlakov, Ivan Pavlovic Shestakov

Publication date: 1974

Published in: Algebra and Logic (Search for Journal in Brave)

Full work available at URL: http://www.rusdml.de/en/rdms/rimg/?PPN=PPN394930762_0012&DMDID=DMDLOG_0006

Mathematics Subject Classification ID

General nonassociative rings (17A99) Structure theory for Jordan algebras (17C10) Alternative rings (17D05) Noncommutative Jordan algebras (17A15) Nonassociative algebras satisfying other identities (17A30) Other nonassociative rings and algebras (17D99)

Related Items (31)

Algebraic rings with compact topology ⋮ Heredity of radicals in a class of noncommutative Jordan rings ⋮ Binary-(-1,1)-nilalgebras ⋮ Hereditariness of radicals in the class of right-alternative almost alternative rings ⋮ Constructions of special radicals of algebras ⋮ Absolute zero-divisors and algebraic Jordan algebras ⋮ Decomposition of a compact ring into the sum of the radical and an inertial subring ⋮ The weakly solvable radical and locally strongly algebraic derivations of locally generalized special Lie algebras ⋮ The Kostrikin radical and similar radicals of Lie algebras ⋮ Nilpotency in Jordan and right alternative algebras ⋮ Identities of finite Jordan \(\Phi\)-algebras ⋮ A Jordan algebra of a Mal'tsev algebra ⋮ Heredity of radicals and ideals of algebras generated by subideals and subinvariant subalgebras ⋮ Local finiteness of algebras ⋮ Nonassociative rings ⋮ Algebraic Lie algebras of bounded degree ⋮ Nilpotency of ideals in (-1,1) rings with minimum condition ⋮ Solvability of (-1,1) nil rings ⋮ Almost alternative algebras ⋮ A free \((-1, 1)\)-algebra with two generators ⋮ Right alternative rings ⋮ Radicals of Jordan rings connected with alternative rings ⋮ Locally finite coalgebras and the locally nilpotent radical. I ⋮ Locally Noetherian and locally representable varieties of alternative algebras ⋮ A locally nilpotent radical in some classes of right-alternative rings ⋮ Nilpotency of the associator ideal of a free finitely generated (-1, 1) ring ⋮ Absolute zero-divisors and radicals of finitely generated alternative algebras ⋮ Mal'tsev algebras ⋮ Heredity of radicals of rings of type \((\gamma,\delta)\) ⋮ Nil rings of type (gamma,delta) ⋮ Compact nonassociative rings

Cites Work

• Ideals in semiprime alternative rings
• Nucleus and center alternativ rings
• The Levitzki radical in varieties of algebras
• Nil semi-simple (-1,1) rings
• Hereditary Radicals in Associative and Alternative Rings
• On Rings with Completely Alternative Commutators
• Primitive Alternative Rings and Semi-Simplicity
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