Invariant basis numberIn mathematics, more specifically in the field of ring theory, a ring has the invariant basis number (IBN) property if all finitely generated free left modules over R have a well-defined rank. In the case of fields, the IBN property becomes the statement that finite-dimensional vector spaces have a unique dimension. A ring R has invariant basis number (IBN) if for all positive integers m and n, Rm isomorphic to Rn (as left R-modules) implies that m = n.
End-to-end principleThe end-to-end principle is a design framework in computer networking. In networks designed according to this principle, guaranteeing certain application-specific features, such as reliability and security, requires that they reside in the communicating end nodes of the network. Intermediary nodes, such as gateways and routers, that exist to establish the network, may implement these to improve efficiency but cannot guarantee end-to-end correctness.
Network block deviceOn Linux, network block device (NBD) is a network protocol that can be used to forward a block device (typically a hard disk or partition) from one machine to a second machine. As an example, a local machine can access a hard disk drive that is attached to another computer. The protocol was originally developed for Linux 2.1.55 and released in 1997. In 2011 the protocol was revised, formally documented, and is now developed as a collaborative open standard. There are several interoperable clients and servers.
Fixed-point subringIn algebra, the fixed-point subring of an automorphism f of a ring R is the subring of the fixed points of f, that is, More generally, if G is a group acting on R, then the subring of R is called the fixed subring or, more traditionally, the ring of invariants under G. If S is a set of automorphisms of R, the elements of R that are fixed by the elements of S form the ring of invariants under the group generated by S. In particular, the fixed-point subring of an automorphism f is the ring of invariants of the cyclic group generated by f.
Ring theoryIn algebra, ring theory is the study of rings—algebraic structures in which addition and multiplication are defined and have similar properties to those operations defined for the integers. Ring theory studies the structure of rings, their representations, or, in different language, modules, special classes of rings (group rings, division rings, universal enveloping algebras), as well as an array of properties that proved to be of interest both within the theory itself and for its applications, such as homological properties and polynomial identities.
