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 …

Let A=⊕ α∈ Γ A α and B=⊕ α∈ Γ B α be two commutative rings graded by an arbitrary
commutative monoid Γ, let J be a homogeneous ideal of B and f: A→ B a graded ring …

In this paper, the $\tau_q $-weak global dimension $\tau_q $-\cwd $(R) $ of a commutative
ring $ R $ is introduced. Rings with $\tau_q $-weak global dimension equal to $0 $ are …

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Diaspora Journal of Mathematics Volume 14, Number 1, pp. 119–125 (2012) ISSN 1539-854X …

Let R and S be commutative rings with identity, J be an ideal of S, and let f: R→ S be a ring
homomorphism. The amalgamation of R with S along J with respect to f denoted by R⋈ f J …

arXiv:1109.6054v1 [math.AC] 27 Sep 2011 Page 1 arXiv:1109.6054v1 [math.AC] 27 Sep 2011
AMALGAMATED ALGEBRA EXTENSIONS DEFINED BY VON NEUMANN REGULAR AND …

Within the last decade, much attention in commutative ring theory has been drawn into the
revitalized concept of an “amalgamated duplication of a ring along an ideal,” also known …

In [21], Jhilal and Mahdou defined a commutative unital ring R to be an (n, d)-perfect ring, if
every n-presented module with flat dimension at most d, has projective dimension at most d …

Let f: A→ B be a ring homomorphism, J be an ideal of B and A⋈ f J the amalgamation of A
with B along J with respect to f. In this paper, we provide necessary and sufficient conditions …