The graph of zero-divisors of quadratic quotients of Rees algebras

DOI10.1080/00927872.2021.1930025zbMath1477.13020OpenAlexW3168294825MaRDI QIDQ5160024

Sara Caffarelli, Carmelo Antonio Finocchiaro

Publication date: 28 October 2021

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927872.2021.1930025

zbMATH Keywords

complete graphzero-divisor graphamalgamated duplicationNagata's idealization

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Ideals and multiplicative ideal theory in commutative rings (13A15) Extension theory of commutative rings (13B02) General commutative ring theory and combinatorics (zero-divisor graphs, annihilating-ideal graphs, etc.) (13A70)

Cites Work

• Unnamed Item
• A construction of Gorenstein rings
• On the diameter and girth of a zero-divisor graph
• The amalgamated duplication of a ring along a multiplicative-canonical ideal
• The minimal prime spectrum of a reduced ring
• Coloring of commutative rings
• The zero-divisor graph of a commutative ring
• Beck's coloring of a commutative ring
• Zero-divisor graphs of amalgamated duplication of a ring along an ideal
• The diameter of a zero divisor graph
• Zero-divisor graphs of idealizations
• CYCLES AND SYMMETRIES OF ZERO-DIVISORS
• AN AMALGAMATED DUPLICATION OF A RING ALONG AN IDEAL: THE BASIC PROPERTIES
• A Family of Quotients of the Rees Algebra
• New algebraic properties of quadratic quotients of the Rees algebra

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