Please avoid saying; "the linux kernel", as that's the pattern used to name most OS kernels (in most OS's, the kernel doesn't have a particular name, so such is usually named by saying; the <OS-name> kernel, for example; the NT kernel), so by saying such, you imply that Linux is an OS.
Please say; "the kernel, Linux", "Linux, the kernel" or just Linux when referring to Linux - as there's usually no need for mentioning "kernel" redundantly.