irreducible element

irreducible element

[‚ir·ə′düs·ə·bəl ′el·ə·mənt]
(mathematics)
An element x of a ring which is not a unit and such that every divisor of x is improper.
References in periodicals archive ?
I personally would have preferred that Brower had made his own position on these matters explicit--especially since history, rather like psychical research, depends on good faith and contains an irreducible element of indeterminacy.
This is the source of the infinity of all objects of knowledge, as well as of the irreducible element of faith, trust or belief required of all the ideas, if not indeed an element of fiction understood as an active process: the ideas are in a sense always fashioned.
The musical object should be considered apart from the conditions of its social use as an irreducible element of its social meaning.
One more example (introducing the idea of contradictions): 'The contradictory is an irreducible element of human life as we all experience it.
Faris's criteria are: the presence of an irreducible element of magic; the presence of the phenomenal world; unsettling doubts in the reader to explain the nature of the events; the merging in the narrative of different realms; disruptions of time, space and identity.
The first chapter, entitled "Definitions and Locations," pinpoints "magic" as the irreducible element coexisting with people's everyday activities in the natural world.
The theme of the ineffability of the infinitely individuated and the idea of an irreducible element of realism within idealism mentioned earlier constitute a fitting transition to the concluding essay by Karl Ameriks, "The Legacy of Idealism in the Philosophy of Feuerbach, Marx, and Kierkegaard.
The relation between Jews and Christians includes an irreducible element of dispute and even rivalry.
170) eschews liberalism's strict division between the public and private spheres-"we understand the public realm not as a discrete area but rather as an irreducible element of all human activities" (p.
The reconstruction of Asante modes of thought necessarily depends, to a significant degree, upon twentieth-century rather than pre-colonial evidence; although extrapolation from this material backwards into earlier times is systematically tested against what can be squeezed out of contemporary records, the procedure involves an irreducible element of speculativeness - especially given McCaskie's own stress on the radical disjunction in Asante historical experience represented by the dissolution of the state structure in the civil wars of the 1880s.
And, in spite of many problems built into the research program that arose from this model, Petruccioli sees the significance of Bohr's contribution in his introduction of the concept of discontinuity as an essential and irreducible element in atomic physics.