Nil skew α-Armendariz amalgamated rings

Subject Areas : Statistics

Negin Farshad ¹ , Shaaban Ali Safarisabet ² , Ahmad Moussavi ³

1 - Department of Mathematics, Islamic Azad University, Central Tehran Branch, Tehran, Iran
2 - Department of Mathematics, Islamic Azad University, Central Tehran Branch, Tehran, Iran
3 - Faculty of Mathematical Sciences, Department of Pure Mathematics, Tarbiat Modares University, Tehran, Iran

Received: 2021-06-07 Accepted : 2021-09-13 Published : 2024-01-18

Keywords: -آرمنداریز اریب ضعیف, 2-اولیه, آرمنداریز اریب پوچ, &alpha, حلقه در هم آمیخته, -&alpha,

Abstract :

Let f :A→B be a ring homomorphism and K an ideal of B. In this paper we determine the endomorphism α of the amalgamation ring A⋈^f K of A and B along K with respect to f. Then we investigate some annihilation properties, such as nil skew α-Armendariz, and weak skew α-Armendariz, of the amalgamation ring A⋈^f K. We show the relations among A , f(A)+K and the amalgamation ring A⋈^f K, in terms of their nil skew Armendariz and weak skew Armendariz properties. Also we investigate 2-primal property of the amalgamation ring A⋈^f K. Among other results, we show that, if A is a 2-primal α_1-compatible ring and f(A) +K is a 2-primal α_2-compatible ring, then the amalgamation ring A⋈^f K is a nil skew α-Armendariz ring, where α_1 and α_2 are endomorphisms of A and f(A)+K, respectively, and α is the endomorphism on A⋈^f K induced by α_1 and α_2.

References:


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