The notation $\mathbb Z_p$ can mean: 1) the ring of $p$-adic numbers 2) the ring $\mathbb Z[\frac 1p]$ 3) the field $\mathbb Z/p\mathbb Z$, but this notation is not advisable. …

There are a few ways to define the $p$-adic numbers. If one defines the ring of $p$-adic integers $\mathbb Z_p$ as the inverse limit of the sequence $(A_n, \phi_n)$ with $A_n:=\mathbb Z/p^n …

2021年3月25日 · I would like to figure out the endomorphism ring of p-adic integer $Z_{p}$. I know $End（Z）$ is isomorphic to $Z$ , And I guess $End（Zp）$ is also $Zp$ .

i= 0 for i<0, easily checked to be a ring via the properties of the norm. The following exercise collects some of the most important properties of Z p. Exercise 1.6. (i) Z p is open and closed …

a ring homomorphism, and its kernel is clearly trivial, since 0 is the only integer congruent to 0 mod pn for all n. Thus the ring Z p has characteristic 0 and contains Z as a subring. But Z pis a …

2025年3月18日 · This Stackable Rings item by MasteRetsaM has 10901 favorites from Etsy shoppers. Ships from Las Vegas, NV.

Return whether self and ring are isomorphic, i.e. whether ring is an implementation of \(\ZZ_p\) for the same prime as self. INPUT: self – a \(p\) -adic ring

2025年1月12日 · The marking "ZP" on a ring likely stands for the metal purity of the ring. In this case, "ZP" may indicate that the ring is made of zinc alloy plated with another metal, such as …

A ring is a mathematical construction in which there are well-behaved notions of addition and multiplication; if you’ve never heard of them before, you probably just need to know about …

2021年12月6日 · If by $\mathbb{Z}_p$ you mean $\mathbb{Z}_p$ (the ring of $p$-adic integers): You can identify elements in $\mathbb{Z}_p$ as formal power series in $p$ with coefficients in …