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Let [Formula: see text] be a pure number field generated by a complex root [Formula: see text] of a monic irreducible polynomial [Formula: see text] where [Formula: see text] is a square free rational integer, [Formula: see text] is a rational prime integer, and [Formula: see text] is a positive integer. In this paper, we study the monogenity of [Formula: see text]. We prove that if [Formula: see text], then [Formula: see text] is monogenic. But if [Formula: see text] and [Formula: see text], then [Formula: see text] is not monogenic. Some illustrating examples are given.

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Let K ¼ QðaÞ be a pure number field generated by a complex root a of a monic irreducible polynomial FðxÞ ¼ x 42 À m 2 Z½x, where m 6 ¼ AE1 is a square-free rational integer. In this paper, we study the monogenity of K. We prove that if m 6 1 ðmod4Þ, m 6 Ç1 ðmod9Þ, and m 6 2 fÇ1; 18; 19; 30; 31g ðmod49Þ, then K is monogenic. But, if m 1 ðmod4Þ, or m 1 ðmod9Þ, or m 1 ðmod49Þ, then K is not monogenic. Our results are illustrated by some examples.

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