Let R and S be commutative rings with identity, f: R→ S a ring homomorphism and J an ideal
of S. Then the subring R⋈ f J:={(r, f (r)+ j)| r∈ R and j∈ J} of R× S is called the amalgamation …

In this paper we improve the recent results on the transfer of Pr\" ufer, Gaussian and
arithmetical conditions on amalgamated constructions. As an application we provide an …

Let A and B be Banach algebras, θ: A → B θ: A→ B be a continuous Banach algebra
homomorphism and I be a closed ideal in B. Then the direct sum of A and I with respect to θ …

Let A and B be commutative rings with unity, f:A→B a ring homomorphism and J an ideal of
B. Then, the subring A⋈^fJ:={(a,f(a)+j)∣a∈A and j∈J\} of A*B is called the amalgamation of …

Let R and S be commutative rings with identity, f: R→ S a ring homomorphism and J an ideal
of S. Then, the subring R⋈ f J:={(a, f (a)+ j)| a∈ R and j∈ J} of R× S is called the …

Let be a ring homomorphism and J be an ideal of S. Then the subring and of is called the
amalgamation of R with S along J with respect to f. In this paper, we characterize when is a …

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Let R and S be commutative rings with identity, J an ideal of S, and f: R→ S a ring
homomorphism. In this paper, we determine the set of associated prime ideals of …

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

Let $ R $ and $ S $ be commutative rings with unity, $ f\colon R\rightarrow S $ a ring
homomorphism and $ J $ an ideal of $ S $. Then the subring $ R\bowtie^ fJ:=\lbrace (a, f …