Calculation of Tor for module with trivial action
$begingroup$
Let $S$ be a ring of the form $mathbb{Z}/p[x] otimes_{mathbb{Z}/p}E(y)$. Where $mathbb{Z}/p[x]$ is the polynomial algebra and $E(y)$ is the exterior algebra over $mathbb{Z}/p$. Consider $bar{S},$ a $S$-module with trivial $S$-module structure on $S$. Then I want to proof the following formula $$Tor^S(bar{S}, mathbb{Z}/p) cong S otimes Tor^S(mathbb{Z}/p, mathbb{Z}/p).$$
Any hint will be appreciated. Thank you in advance.
abstract-algebra ring-theory modules homological-algebra projective-module
asked Dec 6 '18 at 7:56
SurojitSurojit
393110
$endgroup$
add a comment |
$begingroup$
Let $S$ be a ring of the form $mathbb{Z}/p[x] otimes_{mathbb{Z}/p}E(y)$. Where $mathbb{Z}/p[x]$ is the polynomial algebra and $E(y)$ is the exterior algebra over $mathbb{Z}/p$. Consider $bar{S},$ a $S$-module with trivial $S$-module structure on $S$. Then I want to proof the following formula $$Tor^S(bar{S}, mathbb{Z}/p) cong S otimes Tor^S(mathbb{Z}/p, mathbb{Z}/p).$$
Any hint will be appreciated. Thank you in advance.
abstract-algebra ring-theory modules homological-algebra projective-module
asked Dec 6 '18 at 7:56
SurojitSurojit
393110
$endgroup$
add a comment |
$begingroup$
Let $S$ be a ring of the form $mathbb{Z}/p[x] otimes_{mathbb{Z}/p}E(y)$. Where $mathbb{Z}/p[x]$ is the polynomial algebra and $E(y)$ is the exterior algebra over $mathbb{Z}/p$. Consider $bar{S},$ a $S$-module with trivial $S$-module structure on $S$. Then I want to proof the following formula $$Tor^S(bar{S}, mathbb{Z}/p) cong S otimes Tor^S(mathbb{Z}/p, mathbb{Z}/p).$$
Any hint will be appreciated. Thank you in advance.
abstract-algebra ring-theory modules homological-algebra projective-module
asked Dec 6 '18 at 7:56
SurojitSurojit
393110
$endgroup$
Let $S$ be a ring of the form $mathbb{Z}/p[x] otimes_{mathbb{Z}/p}E(y)$. Where $mathbb{Z}/p[x]$ is the polynomial algebra and $E(y)$ is the exterior algebra over $mathbb{Z}/p$. Consider $bar{S},$ a $S$-module with trivial $S$-module structure on $S$. Then I want to proof the following formula $$Tor^S(bar{S}, mathbb{Z}/p) cong S otimes Tor^S(mathbb{Z}/p, mathbb{Z}/p).$$
Any hint will be appreciated. Thank you in advance.
abstract-algebra ring-theory modules homological-algebra projective-module
abstract-algebra ring-theory modules homological-algebra projective-module
asked Dec 6 '18 at 7:56
SurojitSurojit
393110
asked Dec 6 '18 at 7:56
SurojitSurojit
393110
asked Dec 6 '18 at 7:56
SurojitSurojit
393110
asked Dec 6 '18 at 7:56
SurojitSurojit
393110
asked Dec 6 '18 at 7:56
SurojitSurojit
393110
393110
add a comment |
add a comment |
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