Totally real number field

The number field Q(√2) sits inside R, and the two embeddings of the field into C send every element in the field to another element of R, hence the field is totally real.

In number theory, a number field K is called totally real if for each embedding of K into the complex numbers the image lies inside the real numbers. Equivalent conditions are that K is generated over Q by one root of an integer polynomial P, all of the roots of P being real; or that the tensor product algebra of K with the real field, over Q, is a product of copies of R.

单词	Totally real
释义	Totally real 原声例句摩登家庭第一季_Modern Family-Season01 But they can be totally real, right? Like Anne Frank's? 但有可能完全是真的，对吧？像《安妮日记》那样。 Life Noggin This seems like a totally real scenario. 这似乎是一个完全真实的场景。冷知识百科大全 History Channel movie, this was actually totally real. 历史频道的电影，这实际上是完全真实的。 BuzzFeedViolet Actors didn't exist. Characters were totally real. 演员不存在。人物是完全真实的。话唠橙的日常 Oh, not at all! The TNT is totally real. - 哦，一点也不！TNT 是完全真实的。摩登家庭第一季有字幕 361.But they can be totally real, right? 但有可能完全是真的对吧？ Goosebumps鸡皮疙瘩 It felt warm inside, like human skin, and the mouse fur on the outside felt totally real. 里面感觉很温暖，就像人的皮肤一样，外面的老鼠毛感觉起来完全是真的。简单心理学 You see, one 2002 study found that when put under hypnosis, some people could master the Stroop task by becoming convinced that the totally real and normal English words they were presented, were gibberish. 2002 年的一项研究发现，处于催眠状态时，有些人可以通过使自己认为，呈现给他们的那些英语单词都是胡言乱语，以此来掌握 Stroop 的任务。英语百科 Totally real number field In number theory, a number field K is called totally real if for each embedding of K into the complex numbers the image lies inside the real numbers. Equivalent conditions are that K is generated over Q by one root of an integer polynomial P, all of the roots of P being real; or that the tensor product algebra of K with the real field, over Q, is a product of copies of R.
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