Cyclic moduleIn mathematics, more specifically in ring theory, a cyclic module or monogenous module is a module over a ring that is generated by one element. The concept is a generalization of the notion of a cyclic group, that is, an Abelian group (i.e. Z-module) that is generated by one element. A left R-module M is called cyclic if M can be generated by a single element i.e. M = (x) = Rx = {rx r ∈ R} for some x in M. Similarly, a right R-module N is cyclic if N = yR for some y ∈ N. 2Z as a Z-module is a cyclic module.
Category of modulesIn algebra, given a ring R, the category of left modules over R is the whose are all left modules over R and whose morphisms are all module homomorphisms between left R-modules. For example, when R is the ring of integers Z, it is the same thing as the . The category of right modules is defined in a similar way. One can also define the category of bimodules over a ring R but that category is equivalent to the category of left (or right) modules over the enveloping algebra of R (or over the opposite of that).
Artinian ringIn mathematics, specifically abstract algebra, an Artinian ring (sometimes Artin ring) is a ring that satisfies the descending chain condition on (one-sided) ideals; that is, there is no infinite descending sequence of ideals. Artinian rings are named after Emil Artin, who first discovered that the descending chain condition for ideals simultaneously generalizes finite rings and rings that are finite-dimensional vector spaces over fields.
PedestrianA pedestrian is a person traveling on foot, whether walking or running. In modern times, the term usually refers to someone walking on a road or pavement, but this was not the case historically. The meaning of pedestrian is displayed with the morphemes ped- ('foot') and -ian ('characteristic of'). This word is derived from the Latin term pedester ('going on foot') and was first used (in English language) during the 18th century. It was originally used, and can still be used today, as an adjective meaning plain or dull.
Viable system modelThe viable system model (VSM) is a model of the organizational structure of any autonomous system capable of producing itself. A viable system is any system organised in such a way as to meet the demands of surviving in the changing environment. One of the prime features of systems that survive is that they are adaptable. The VSM expresses a model for a viable system, which is an abstracted cybernetic (regulation theory) description that is claimed to be applicable to any organisation that is a viable system and capable of autonomy.
Pedestrian crossingA pedestrian crossing (or crosswalk in American English) is a place designated for pedestrians to cross a road, street or avenue. The term "pedestrian crossing" is also used in the Vienna and Geneva Conventions, both of which pertain to road signs and road traffic. Marked pedestrian crossings are often found at intersections, but may also be at other points on busy roads that would otherwise be too unsafe to cross without assistance due to vehicle numbers, speed or road widths.
Viable system theoryViable system theory (VST) concerns cybernetic processes in relation to the development/evolution of dynamical systems. They are considered to be living systems in the sense that they are complex and adaptive, can learn, and are capable of maintaining an autonomous existence, at least within the confines of their constraints. These attributes involve the maintenance of internal stability through adaptation to changing environments. One can distinguish between two strands such theory: formal systems and principally non-formal system.
Pedestrian zonePedestrian zones (also known as auto-free zones and car-free zones, as pedestrian precincts in British English, and as pedestrian malls in the United States and Australia) are areas of a city or town reserved for pedestrian-only use and in which most or all automobile traffic is prohibited. Converting a street or an area to pedestrian-only use is called pedestrianisation.
