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In [[mathematics]], a '''supercommutative algebra''' is a [[superalgebra]] (i.e. a '''Z'''<sub>2</sub>-[[graded algebra]]) such that for any two [[homogeneous element]]s ''x'', ''y'' we have
 
:<math>yx = (-1)^{|x| |y|}xy.\,</math>
 
Equivalently, it is a superalgebra where the [[supercommutator]]
 
:<math>[x,y] = xy - (-1)^{|x| |y|}yx\,</math>
 
always vanishes. Algebraic structures which supercommute in the above sense are sometimes referred to as '''skew-commutative associative algebras''' to emphasize the anti-commutation, or, to emphasize the grading, '''graded-commutative''' or, if the supercommutativity is understood, simply '''commutative'''.
 
Any [[commutative algebra]] is a supercommutative algebra if given the trivial gradation (i.e. all elements are even). [[Grassmann algebra]]s (also known as [[exterior algebra]]s) are the most common examples of nontrivial supercommutative algebras. The '''supercenter''' of any superalgebra is the set of elements that supercommute with all elements, and is a supercommutative algebra.
 
The [[even subalgebra]] of a supercommutative algebra is always a [[commutative algebra]]. That is, even elements always commute. Odd elements, on the other hand, always anticommute. That is,
:<math>xy + yx = 0\,</math>
for odd ''x'' and ''y''. In particular, the square of any odd element ''x'' vanishes whenever 2 is invertible:
:<math>x^2 = 0.\,</math>
Thus a commutative superalgebra (with 2 invertible and nonzero degree one component) always contains [[nilpotent]] elements.
 
==See also==
*[[Commutative algebra]]
*[[Lie superalgebra]]
 
{{DEFAULTSORT:Supercommutative Algebra}}
[[Category:Algebras]]
[[Category:Super linear algebra]]

Revision as of 06:40, 26 February 2014

If you have the desire to process settings swiftly, loading files fast, however, the body is logy plus torpid, what would we do? If you are a giant "switchboard" which is lack of efficient management system and efficient housekeeper, what would we do? If you have send the exact commands to your notice, nevertheless the body cannot work correctly, what would we do? Yes! You want a full-featured repair registry!

Google Chrome crashes on Windows 7 by the corrupted cache contents and difficulties with the stored browsing information. Delete the browsing information and well-defined the contents of the cache to solve this issue.

So what if you look for whenever we compare registry cleaners. Many of the registry cleaners accessible today, have surprisingly synonymous features. The leading ones which you should be shopping for are these.

Windows errors may be caused by any number of reasons, but there's virtually always one cause. There's a hidden part of the program that is responsible for making 90% of all Windows mistakes, plus it's called the 'registry'. This really is the central database for the system plus is where a computer stores all its program files and settings. It's a fairly important piece of Windows, which is should be able to function. However, it's furthermore among the biggest causes of difficulties on the PC.

Another popular cause of PC slow down is a corrupt registry. The registry is a rather important component of computers running on Windows platform. When this gets corrupted a PC will slowdown, or worse, not start at all. Fixing the registry is simple with all the use of a system and tuneup utilities.

Another element is registry. It is regarded as the many important part inside a Windows XP, Vista operating systems. When Windows commence up, it read associated information from registry and load into computer RAM. This takes up a big piece of the startup time. After the information is all loaded, computer runs the business programs.

We require a choice to automatically delete unwelcome registry keys. This may help save you hours of laborious checking by your registry keys. Automatic deletion is a key element whenever you compare registry products.

What I would suggest is to look on the own for registry cleaners. You can do this with a Google search. If you find products, look for reviews plus reviews about the product. Then you are able to see how others like the product, plus how effectively it works.

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