The description of varieties of rings whose finite rings are uniquely determined by their zero-divisor graphs.

DOI10.3103/S1066369X13060029zbMath1284.16027OpenAlexW2056123736MaRDI QIDQ384590

A. S. Kuz'mina, Evgeniĭ Vladimirovich Zhuravlev, Yuriĭ Nikolaevich Mal'tsev

Publication date: 28 November 2013

Published in: Russian Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3103/s1066369x13060029

zbMATH Keywords

polynomial identitieszero-divisor graphsfinite nilpotent ringsvarieties of associative ringssubdirectly irreducible finite rings

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) Nil and nilpotent radicals, sets, ideals, associative rings (16N40) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) (T)-ideals, identities, varieties of associative rings and algebras (16R10)

Related Items (6)

Describing ring varieties in which all finite rings have Hamiltonian zero-divisor graphs. ⋮ Compressed zero-divisor graphs of finite associative rings ⋮ Compressed and partially compressed zero-divisor graphs of finite associative rings ⋮ On zero-divisor graphs of skew polynomial rings over non-commutative rings ⋮ On zero divisor graphs of finite commutative local rings ⋮ On zero-divisors of near-rings of polynomials

Cites Work

• Unnamed Item
• Coloring of commutative rings
• The zero-divisor graph of a commutative ring
• On the zero-divisor graph of a commutative ring
• On zero-divisor graphs of finite rings.
• ON VARIETIES OF RINGS WHOSE FINITE RINGS ARE DETERMINED BY THEIR ZERO-DIVISOR GRAPHS

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