Sentence examples for regular ring from inspiring English sources

Let $R \to \Lambda $ be a regular ring map.

Let $A \to B \to C$ be regular ring maps.

Observe that $k[x_1, \ldots, x_ n]$ is a regular ring by Algebra, Proposition 10.113.2.

Then $k \to K$ is a regular ring map if and only if $K$ is a separable field extension of $k$.

Key examples of the talk will be regular ring spectra, gorenstein ring spectra and if time permits complete intersection ring spectra.

The same entry in aprotic DMFA afforded regular ring cleavage product [B12H11OCH2CH2OCH2CH2CN]2. Subsequent work up of this nitrile with sodium methanolate in MeOH led to the alcohol ([B12H11OCH2CH2OH]2−) as well.

Pure α and β form of PBA can form regular ring-banded spherulites.

We use one of them here in order to generate a series of networks: Watts and Strogatz described a rewiring procedure by which a regular ring-lattice is randomly rewired by which it becomes a small-world network [24].

Both C and L parameters for AD and control groups are plotted together with the theoretical values for random and ordered (regular) ring-like networks (Figure 3a d; ordered graph: C = 3/4, L = N/2K; random graph: C = K/N, L = ln(N /ln(K)).

Consider binary consensus over an L-regular ring lattice.

In this paper, we investigate properties of abelian strongly k-Engel π-regular ring.