How to know the kernel version of a SAP R3 system?

From any screen choose System-->Status then click the 'other kernel info' icon (between Navigate and Cancel).

The same information can be found at OS level in the dispatcher trace file: /usr/sap///work/dev_disp.

Goto transaction sm51, and click (not double click) on the the Database
server and then click on release notes. there you will see the SAP R/3
kernel and patch level etc.

You can use the System ==> Status and then Other
Kernel Info button to get the details about the Kernel
Release, Patch levels etc.

I think an even more convenient way to do this is to use SM51. Highlight
the server you are interested in and click on "Release Information". This
provides you a location to view all servers with out logging on to each
one.

The answer below will give you information about the server you are
connected to only.

Also try "disp+work -v" on server.

go to transaction SM51 -->release information