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The nilradical of a commutative ring is the set of all nilpotent elements in the ring, or equivalently the radical of the zero ideal.This is an ideal because the sum of any two nilpotent elements is nilpotent (by the binomial formula), and the product of any element with a nilpotent element is nilpotent (by commutativity).
Radical politics denotes the intent to transform or replace the fundamental principles of a society or political system, often through social change, structural change, revolution or radical reform. [1] The process of adopting radical views is termed radicalisation.
Advanced Placement (AP) United States Government and Politics (often shortened to AP Gov or AP GoPo and sometimes referred to as AP American Government or simply AP Government) is a college-level course and examination offered to high school students through the College Board's Advanced Placement Program.
Advanced Placement (AP) Macroeconomics (also known as AP Macro and AP Macroecon) is an Advanced Placement macroeconomics course for high school students that culminates in an exam offered by the College Board. Study begins with fundamental economic concepts such as scarcity, opportunity costs, production possibilities, specialization ...
If R is commutative, the Jacobson radical always contains the nilradical. If the ring R is a finitely generated Z-algebra, then the nilradical is equal to the Jacobson radical, and more generally: the radical of any ideal I will always be equal to the intersection of all the maximal ideals of R that contain I. This says that R is a Jacobson ring.
Advanced Placement (AP) Economics (also known as AP Econ) refers to two College Board Advanced Placement Program courses and exams addressing various aspects of the field of economics: AP Macroeconomics
Advanced Placement (AP) Comparative Government and Politics (also known as AP CoGo or AP CompGov) is an Advanced Placement comparative politics course and exam offered by the College Board. It was first administered in 1987.
Originally, political economy meant the study of the conditions under which production or consumption within limited parameters was organized in nation-states. In that way, political economy expanded the emphasis on economics, which comes from the Greek oikos (meaning "home") and nomos (meaning "law" or "order"). Political economy was thus ...