Ordered Rings and Fields - University of Arizona Math
... 23 − 143 ≈ −0.005168744299, which is clearly negative, so we can conclude that 143 is larger. Thus, given any two elements x, y ∈ R\{0}, we can determine which element is greater simply by determining whether x − y is positive or negative. Hence, the entire problem of ordering elements boils down to ...
... 23 − 143 ≈ −0.005168744299, which is clearly negative, so we can conclude that 143 is larger. Thus, given any two elements x, y ∈ R\{0}, we can determine which element is greater simply by determining whether x − y is positive or negative. Hence, the entire problem of ordering elements boils down to ...
3. Modules
... Example 3.8 (Modules over polynomial rings). Let R be a ring. Then an R[x]-module M is the same as an R-module M together with an R-module homomorphism ϕ : M → M: “⇒” Let M be an R[x]-module. Of course, M is then also an R-module. Moreover, multiplication with x has to be R-linear, so ϕ : M → M, m 7 ...
... Example 3.8 (Modules over polynomial rings). Let R be a ring. Then an R[x]-module M is the same as an R-module M together with an R-module homomorphism ϕ : M → M: “⇒” Let M be an R[x]-module. Of course, M is then also an R-module. Moreover, multiplication with x has to be R-linear, so ϕ : M → M, m 7 ...
![Math 110B HW §5.3 – Solutions 3. Show that [−a, b] is the additive](http://s1.studyres.com/store/data/017359919_1-72a70245febeadd05992d7dba1b6dd48-300x300.png)