The primal element in integral domain | ||
| basrah journal of science | ||
| Article 16, Volume 34, Issue 3, December 2016, Pages 170-181 PDF (0 K) | ||
| Author | ||
| Sinan O. Al-Salihi | ||
| Abstract | ||
| An element x of an integral domain R is called primal if whenever x divides a product a1a2 with a1 , a2∈ R, x can be written as x = x1x2 such that xi divides ai ,i =1,2.We study whenin X2 primal in A + X B[X] or A + X B[[X]], when A ⊆ B be an extension of domains. Also we show that if A is an integral domain and S ⊆ A a splitting multiplicative system, then A+XAS[X] is a semirigid GCD-domain if and only if A is a semirigid GCD-domain and for each two elements of S, one of them divides the other. | ||
| Keywords | ||
| Integral Domain; Primal element; Principle ideal; Semirigid GCD; Domains | ||
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