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- W2892091322 abstract "In this paper, we investigate the unit groups of the quotient rings of the integer rings $R_d$ of the quadratic fields $mathbb{Q}(sqrt{d})$ over the rational number field $mathbb{Q}$ . By employing the polynomial expansions and the theory of finite groups, we completely determine the unit groups of $R_d/langlevartheta^nrangle$ for $d=-3$ , $-7$ , $-11$ , $-19$ , $-43$ , $-67$ , $-163$ , where $vartheta$ is a prime in $R_d$ , and $n$ is an arbitrary positive integer. The results in this paper generalize the study of the unit groups of $R_d/langlevartheta^nrangle$ for $d=-1$ , which obtained by J. T. Cross (1983), G. H. Tang and H. D. Su (2010) and for the case $d=-2$ by Y. J. Wei (2016)." @default.
- W2892091322 created "2018-09-27" @default.
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- W2892091322 date "2018-07-15" @default.
- W2892091322 modified "2023-09-23" @default.
- W2892091322 title "ON THE UNIT GROUPS OF THE QUOTIENT RINGS OF IMAGINARY QUADRATIC NUMBER RINGS" @default.
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