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is a short exact sequence of vector spaces, then

is an exact sequence of graded vector spaces [15] as is

In particular, the exterior algebra of a direct sum is isomorphic to the tensor product of the exterior algebras:

This is a graded isomorphism; i.e.,

Slightly more generally, if

is a short exact sequence of vector spaces then Λ k (V) has a filtration

with quotients: F p + 1 / F p = Λ k p ( U ) Λ p ( W ) {\displaystyle F^{p+1}/F^{p}=\Lambda ^{k-p}(U)\otimes \Lambda ^{p}(W)} . In particular, if U is 1-dimensional then

is exact, and if W is 1-dimensional then

is exact. [17]

If K is a field of characteristic 0, [18] then the exterior algebra of a vector space V can be canonically identified with the vector subspace of T( V ) consisting of antisymmetric tensors . Recall that the exterior algebra is the quotient of T( V ) by the ideal I generated by x x .

Let T r ( V ) be the space of homogeneous tensors of degree r . This is spanned by decomposable tensors

The antisymmetrization (or sometimes the skew-symmetrization ) of a decomposable tensor is defined by

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of permutations on the symbols {1, ..., r }. This extends by linearity and homogeneity to an operation, also denoted by Alt, on the full tensor algebra T( V ). The image Alt(T( V )) is the alternating tensor algebra , denoted A( V ). This is a vector subspace of T( V ), and it inherits the structure of a graded vector space from that on T( V ). It carries an associative graded product ^ {\displaystyle {\widehat {\otimes }}} defined by

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¿Medicación necesaria o abuso de drogas?

ADICCIONES

Muchas personas se medican más de la cuenta, pero, ¿realmente es necesario para su salud o es un abuso por adicción?

Mª José Roldán Prieto

No es nuevo que las personas se medican para sentirse mejor, en ocasiones se medican incluso sin preguntarle al médico si lo que se están tomando es lo correcto para su malestar. Hay personas que abusan del alcohol o de los medicamentos para hacer frente al estrés, a algunos dolores físicos y también emocionales.

Es necesario que las personas entiendan que el abuso de las drogas no solo implica el uso indebido de Classic Online Womens Wendy Sling Back Sandals NR Rapisardi Cheap Low Price Sale Original Cheap Newest Marketable For Sale Z4w2G
ilegales, sino que también incluye el abuso de sustancias legales como el alcohol o algunos medicamentos.

Adicto a la medicación

La medicación puede ser considerada como una sustancia que se abusa cuando se utiliza con fines que no estaban destinados para un paciente o cuando se vuelven adicto a los efectos . Tales medicamentos pueden incluso obtenerse en una farmacia fácilmente. Algunos de estos medicamentos pueden contener codeína, ser comprimidos para soportar el dolor y/o jarabes para la tos. Los efectos secundarios del uso de estos medicamentos son que pueden llegar a ser adictivos y que se requieran cantidades cada vez mayores para poder obtener los mismos efectos y la satisfacción de la persona que lo está consumiendo.

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La medicación puede ser considerada como una sustancia que se abusa

Por ejemplo, puede ser fácil convertirse en un adicto a los analgésicos cuando se sufre de dolor crónico. Las personas adictas pueden acudir al médico para obtener la medicina que quieren. Un médico podría no ser consciente de que su paciente también ve otros médicos que están proporcionando las mismas recetas y el paciente podría estar tomando grandes cantidades de medicación, mucho más allá de lo que se requiere para el tratamiento de la enfermedad, pero sí lo suficiente como para causar daño a sus órganos o incluso la muerte a largo plazo.

Este tipo de abuso de sustancias es mucho más sutil e insidioso y, a largo plazo puede ser muy peligroso para la vida de la persona. Esta consecuencia fatal normalmente no la contemplan las personas adictas que solo quieren satisfacer sus sentimientos de adicción para encontrar el bienestar. Este tipo de personas pueden tener gran dificultad en entender que tienen dependencia o una adicción que requiere de un tratamiento intensivo, antes de que empiecen a sufrir los efectos secundarios por abusar de este tipo de sustancias.

Es muy importante que las personas sean conscientes que el abuso de sustancias o medicación no es una opción correcta para tratar sus dolencias

La dependencia a la medicación puede ser causada por la codeína, la oxicodona y las benzodiazepinas . La adicción a estas sustancias puede incluso superar a las drogas ilegales en los centros de adicción, donde las personas acuden para poder trabajar su desintoxicación a este tipo de sustancias.

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