# ideal

### ideal

1. ihanteellinen, ideaalinen

Liittyvät sanat: idealist

## Synonyymisanakirja

### ideal

Liittyvät sanat: idealismi, idealisoida, idealisti, idealistinen.

## Rimmaavat sanat

ideal rimmaa näiden kanssa:

pascal, rial, trial, sial, kajal, sammal, laakasammal, rahkasammal, nukkasammal, maksasammal...

Katso kaikki

## Englannin sanakirja

### ideal englanniksi

1. optimal Optimal; being the best possibility.

2. perfect Perfect, flawless, having no defects.

3. Rambler

4. pertaining Pertaining to ideas, or to a given idea.

5. exist Existing only in the mind; conceptual, imaginary.

6. 1796, Matthew Lewis, The Monk, Folio Society 1985, p. 256:

7. 1818, (w), w:Frankenstein Frankenstein, or the Modern Prometheus,http://en.wikisource.org/wiki/Frankenstein s:Frankenstein/Chapter 4|Chapter 4,

8. Teaching or relating to the doctrine of idealism.

9. the ideal theory or philosophy

10. puhekieltä Not actually present, but considered as present when limits at infinity are included.

11. ideal point

An ideal triangle in the hyperbolic disk is one bounded by three geodesics that meet precisely on the circle.

12. (senseid)A perfect standard of beauty, intellect etc., or a standard of excellence to aim at.

13. Ideals are like stars; you will not succeed in touching them with your hands. But like the seafaring man on the desert of waters, you choose them as your guides, and following them you will reach your destiny - w:Carl Schurz|Carl Schurz

14. puhekieltä A non-empty set|empty lower set (of a partially ordered set) which is closure closed under binary suprema (a.k.a. joins).http://en.wikipedia.org/wiki/Boolean_prime_ideal_theoremPrime_ideal_theorems

15. If (1) the empty set were called a "small" set, and (2) any subset of a "small" set were also a "small" set, and (3) the union of any pair of "small" sets were also a "small" set, then the set of all "small" sets would form an ideal.

16. puhekieltä A subring closed under multiplication by its containing ring.

17. Let $\mathbb\left\{Z\right\}$ be the ring of integers and let $2\mathbb\left\{Z\right\}$ be its ideal of even integers. Then the quotient ring $\mathbb\left\{Z\right\} / 2\mathbb\left\{Z\right\}$ is a Boolean ring.

The product of two ideals $\mathfrak\left\{a\right\}$ and $\mathfrak\left\{b\right\}$ is an ideal $\mathfrak\left\{a b\right\}$ which is a subset of the intersection of $\mathfrak\left\{a\right\}$ and $\mathfrak\left\{b\right\}$. This should help to understand why maximal ideals are prime ideals. Likewise, the union of $\mathfrak\left\{a\right\}$ and $\mathfrak\left\{b\right\}$ is a subset of $\mathfrak\left\{a + b\right\}$.

18. (l)

19. (l) (gloss)

20. an (l)

21. English ideal; perfect standard

22. puhekieltä English ideal; special subsets of a ring