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Given any unital associative -algebra and any - linear map : → such that ()() = 0 for every in , then there exists unital algebra homomorphism : Λ() → such that () = (()) for all in (here is the natural inclusion of in Λ() , see above).

To construct the most general algebra that contains V and whose multiplication is alternating on V , it is natural to start with the most general associative algebra that contains V , the tensor algebra T ( V ) , and then enforce the alternating property by taking a suitable quotient . We thus take the two-sided ideal I in T ( V ) generated by all elements of the form v v for v in V , and define Λ( V ) as the quotient

(and use as the symbol for multiplication in Λ( V )) . It is then straightforward to show that Λ( V ) contains V and satisfies the above universal property.

As a consequence of this construction, the operation of assigning to a vector space V its exterior algebra Λ( V ) is a functor from the category of vector spaces to the category of algebras.

Rather than defining Λ( V ) first and then identifying the exterior powers Λ k ( V ) as certain subspaces, one may alternatively define the spaces Λ k ( V ) first and then combine them to form the algebra Λ( V ) . This approach is often used in differential geometry and is described in the next section.

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R and an R - module M , we can define the exterior algebra Λ( M ) just as above, as a suitable quotient of the tensor algebra T ( M ). It will satisfy the analogous universal property. Many of the properties of Λ( M ) also require that M be a projective module . Where finite dimensionality is used, the properties further require that M be Shop Sale Online Brand New Unisex Sale Online Yves Saint Laurent Leather Wedge Boots Cheapest Price Online Buy Cheap For Sale Buy Cheap Latest UFxbGp5Rf8
and projective. Generalizations to the most common situations can be found in ( Bourbaki 1989 ).

Exterior algebras of vector bundles are frequently considered in geometry and topology. There are no essential differences between the algebraic properties of the exterior algebra of finite-dimensional vector bundles and those of the exterior algebra of finitely generated projective modules, by the Serre–Swan theorem . More general exterior algebras can be defined for sheaves of modules.

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Estoy de acuerdo

Martes, 5 de diciembre de 2017 11:21


El amor no sabe respuestas, pues se trata más bien de una duda constante, de la emoción de la incertidumbre antes de que ésta reviente en tu cara. Y el siguiente poema de Fernanda Bribiesca es prueba de ello.


No me preguntes qué me pasa, porque siempre me pasas tú.

No me preguntes si te quiero porque con sólo tomarnos la mano lo siento.

No me preguntes si me siento bien contigo, porque tú eres lo único que siento.

No me preguntes a dónde me gustaría ir, porque la respuesta es "contigo.

No me digas que soy guapa porque tus ojos me derriten.

No me trates de explicar qué somos, porque cuando nos besamos lo somos todo.

No me debatas sobre si me quieres más, porque no sabes ni cuánto te quiero.

No me expliques otra vez tu vida, pues lo que viene es mejor.


No me trates de convencer de estar contigo, pues yo no me veo en otra parte.

No me intentes cambiar, déjame quererte con todo lo que está mal.

No me expliques cuánto me esperaste, ven a aprovechar cada minuto.

No pienses en qué hacer cuando me vaya, si mi lugar es a tu lado.

No me trates de entender, haz tuyos mis defectos.

No desees que no piense en nosotros, si el nosotros es lo que me encanta.

No me enseñes tus heridas, olvídalas conmigo.


No me ames con medida, hazlo sin lugar a duda.

Escribir y leer poesía es una forma de sanar el alma. Si quieres leer más poemas de amor y desamor, te invitamos a que conozcas a los autores de los poemas para los que se resisten a superar las decepciones y los poemas para los que no quieren olvidar .

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Fernanda Bribiesca

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This JavaScript code creates a simple animation that continually updates the left property of the .item-relative . When you reload the page, you should see the blue image float to the right edge of its container.

This is a pretty rudimentary example, but you can hopefully see how it’s applicable to fancy UI animations. If you were to try to achieve the same effect by manipulating the margin or padding properties, you would inadvertently move the statically positioned boxes and/or the containing .example element, too.

Positioned Elements for Menus

So, those are all the techniques. Let’s do something advanced with them! The rest of this chapter applies our newfound skills towards a fancy navigation menu with an interactive dropdown for one of its links. We’ll be building this page entirely from scratch.

Fixed positioning will let us make the menu stick to the top of the page, and relative positioning will give us an anchor for the absolutely positioned dropdown. We’ll also get a chance to talk about navigation menu best practices and see some practical applications of the pseudo-classes we talked about in CSS Selectors .

For starters, we need a new web page called menu.html that has a header and a simple top-level menu:

Navigation menus should almost always be marked up as a <ul> list instead of a bunch of <div> elements. These semantics make your site’s navigation much more accessible to search engines. Also notice how we’re preparing for our dropdown menu by adding a class attribute to the first <li> in the list. That <span> will allow us to differentiate the label from the submenu it reveals.

Next, we need a new stylesheet called menu.css that makes our .header look a little bit more like a header, among other things:

This should all be familiar, but note the fixed position of the .header , which keeps our navigation menu on top of any content that would go into the page.

Inline Menu Items

Despite being marked up as unordered lists, the navigation menus for most websites don’t actually look like a list. We can fix this by making the list items inline boxes instead of block boxes via the display property. Add the following to menu.css :

We have to use child selectors here instead of descendant selectors because we only want to select <li> elements that are directly inside the .menu . This will become important once we add our submenu, which has its own <li> elements that we don’t want to style with this rule. This snippet also adds margins to all the list items, but removes it from the final <li> using the :last-of-type pseudo-class. This is a pretty common technique for creating margins between items.

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