Abstract
AbstractLet $$f:A\longrightarrow B$$
f
:
A
⟶
B
be a ring homomorphism and J be an ideal of B. The subring $$A\bowtie ^{f}J:=\{(a,f(a)+j)/ a\in A\quad \text {et}\quad j\in J\}$$
A
⋈
f
J
:
=
{
(
a
,
f
(
a
)
+
j
)
/
a
∈
A
et
j
∈
J
}
of $$A\times B$$
A
×
B
is called the amalgamation of A with B along with J with respect to f. In this paper we investigate a general concept of ring with Noetherian spectrum, called S-Noetherian spectrum property which was introduced by Hamed, on the $$A\bowtie ^{f}J$$
A
⋈
f
J
for a multiplicative subset S of $$A\bowtie ^{f}J.$$
A
⋈
f
J
.
Publisher
Springer Science and Business Media LLC
Subject
Geometry and Topology,Algebra and Number Theory
Reference16 articles.
1. Anderson, D.D., Winders, M.: Idealization of a module. Roky Mt. J. Math. 1, 3–56 (2009)
2. Benhissi, A.: Chain Conditions in Commutative Rings, ISBN 978-3-031-09897-0, https:// doi.org/10-1007/978-3-031-09898-7, ISBN 978-3-031-09897-7 (eBook)
3. Anderson, D.D., Dumitrescu, T.: S-Notherian rings. Comm. Algebra 30(9), 4407–4419 (2002)
4. Baeck, G.L., Lim, J.W.: S-Noetherian rings and their extension. Taiwan. J. Math 20(6), 1231–1250 (2016)
5. Chain-Pi, L.: Modules with Noetherian spectrum. Comm. Algebra 38(3), 807–827 (2014). https://doi.org/10.1080/00927870802578050