Zero-divisor graphs in commutative rings Page 1 Zero-divisor graphs in commutative rings
David F. Anderson, Michael C. Axtell, and Joe A. Stickles, Jr. Abstract This article surveys the …

In this book, we introduce several graphical representations of a ring. In the past three
decades, graphs constructed from algebraic structures have been studied extensively by …

Let f: A→ B be a ring homomorphism and let J be an ideal of B. In this paper, we study the
amalgamation of A with B along J with respect to f (denoted by A⋈ fJ), a construction that …

After recalling briefly the main properties of the amalgamated duplication of a ring R along
an ideal I, denoted by R⋈I, see M. D'Anna and M. Fontana, to appear in J. Algebra Appl., we …

Let f: A→ B be a ring homomorphism, and let J be an ideal of B. In this article, we study the
amalgamation of A with B along J with respect to f (denoted by A⋈ f J), a construction that …

Let A⊆ B be a commutative ring extension such that B is a trivial extension of A (denoted by
A∝ E) or an amalgamated duplication of A along some ideal of A (denoted by A⋈ I). This …

Abstract Let f:A→B and g:A→C be two commutative ring homomorphisms, and let J and J' be
two ideals of B and C, respectively, such that f^-1(J)=g^-1(J'). The bi-amalgamation of A with …

This paper investigates ideal-theoretic as well as homological extensions of the Prüfer
domain concept to commutative rings with zero divisors in an amalgamated duplication of a …

A family of quotient rings of the Rees algebra associated to a commutative ring is studied.
This family generalizes both the classical concept of idealization by Nagata and a more …

arXiv:0903.2240v1 [math.AC] 12 Mar 2009 Some homological properties of an amalgamated
duplication of a ring along an ideal Page 1 arXiv:0903.2240v1 [math.AC] 12 Mar 2009 Some …