AN EMBEDDING THEOREM FOR HYPERINTEGRAL DOMAINS

作者：Pianskool S^*; Punkla Y; Hemakul W; Kemprasit Y

来源：Analele Stiintifice ale Universitatii Al I Cuza Din Iasi-Serie Noua-Matematica, 2011, 57(1): 197-206.

• embedding theorem
• hyperintegral domain
• hyperfield

It is well-known that every integral domain D can be embedded in a field F and F is constructed so that F is (up to isomorphism) the smallest field containing D. We extend this result to hyperintegral domains and hyperfields. A commutative Krasner hyperring (A, +, -) is said to be a hyperintegral domain if (A \ {0}, .) is a semigroup and a hyperfield if (A \ {0}, .) is a group. It is shown that every hyperintegral domain (D,+,.) can be embedded in a hyperfield (F, circle plus, circle dot) and the constructed hyperfield (F, circle plus, circle dot) is (up to isomorphism) the smallest hyperfield containing D.

• 出版日期2011