Prime idealIn algebra, a prime ideal is a subset of a ring that shares many important properties of a prime number in the ring of integers. The prime ideals for the integers are the sets that contain all the multiples of a given prime number, together with the zero ideal. Primitive ideals are prime, and prime ideals are both primary and semiprime. An ideal P of a commutative ring R is prime if it has the following two properties: If a and b are two elements of R such that their product ab is an element of P, then a is in P or b is in P, P is not the whole ring R.
Ideal (ring theory)In mathematics, and more specifically in ring theory, an ideal of a ring is a special subset of its elements. Ideals generalize certain subsets of the integers, such as the even numbers or the multiples of 3. Addition and subtraction of even numbers preserves evenness, and multiplying an even number by any integer (even or odd) results in an even number; these closure and absorption properties are the defining properties of an ideal.
Maximal idealIn mathematics, more specifically in ring theory, a maximal ideal is an ideal that is maximal (with respect to set inclusion) amongst all proper ideals. In other words, I is a maximal ideal of a ring R if there are no other ideals contained between I and R. Maximal ideals are important because the quotients of rings by maximal ideals are simple rings, and in the special case of unital commutative rings they are also fields.
Fractional idealIn mathematics, in particular commutative algebra, the concept of fractional ideal is introduced in the context of integral domains and is particularly fruitful in the study of Dedekind domains. In some sense, fractional ideals of an integral domain are like ideals where denominators are allowed. In contexts where fractional ideals and ordinary ring ideals are both under discussion, the latter are sometimes termed integral ideals for clarity. Let be an integral domain, and let be its field of fractions.
Ideal theoryIn mathematics, ideal theory is the theory of ideals in commutative rings. While the notion of an ideal exists also for non-commutative rings, a much more substantial theory exists only for commutative rings (and this article therefore only considers ideals in commutative rings.) Throughout the articles, rings refer to commutative rings. See also the article ideal (ring theory) for basic operations such as sum or products of ideals.
Minimal idealIn the branch of abstract algebra known as ring theory, a minimal right ideal of a ring R is a non-zero right ideal which contains no other non-zero right ideal. Likewise, a minimal left ideal is a non-zero left ideal of R containing no other non-zero left ideals of R, and a minimal ideal of R is a non-zero ideal containing no other non-zero two-sided ideal of R . In other words, minimal right ideals are minimal elements of the partially ordered set (poset) of non-zero right ideals of R ordered by inclusion.
SacrificeSacrifice is the offering of material possessions or the lives of animals or humans to a deity as an act of propitiation or worship. Evidence of ritual animal sacrifice has been seen at least since ancient Hebrews and Greeks, and possibly existed before that. Evidence of ritual human sacrifice can also be found back to at least pre-Columbian civilizations of Mesoamerica as well as in European civilizations. Varieties of ritual non-human sacrifices are practiced by numerous religions today.
NarrativeA narrative, story, or tale is any account of a series of related events or experiences, whether nonfictional (memoir, biography, news report, documentary, travelogue, etc.) or fictional (fairy tale, fable, legend, thriller, novel, etc.). Narratives can be presented through a sequence of written or spoken words, through still or moving images, or through any combination of these. The word derives from the Latin verb narrare (to tell), which is derived from the adjective gnarus (knowing or skilled). Narration (i.
Radical of an idealIn ring theory, a branch of mathematics, the radical of an ideal of a commutative ring is another ideal defined by the property that an element is in the radical if and only if some power of is in . Taking the radical of an ideal is called radicalization. A radical ideal (or semiprime ideal) is an ideal that is equal to its radical. The radical of a primary ideal is a prime ideal. This concept is generalized to non-commutative rings in the Semiprime ring article.
HonourHonour (Commonwealth English) or honor (American English; see spelling differences) is a quality of a person that is both of social teaching and of personal ethos, that manifests itself as a code of conduct, and has various elements such as valour, chivalry, honesty, and compassion. It is an abstract concept entailing a perceived quality of worthiness and respectability that affects both the social standing and the self-evaluation of an individual or of institutions such as a family, school, regiment, or nation.
HistoryHistory (derived ) is the systematic study and documentation of the human past. The period of events before the invention of writing systems is considered prehistory. "History" is an umbrella term comprising past events as well as the memory, discovery, collection, organization, presentation, and interpretation of these events. Historians seek knowledge of the past using historical sources such as written documents, oral accounts, art and material artifacts, and ecological markers.
Human sacrificeHuman sacrifice is the act of killing one or more humans as part of a ritual, which is usually intended to please or appease gods, a human ruler, public or jurisdictional demands for justice by capital punishment, an authoritative/priestly figure or spirits of dead ancestors or as a retainer sacrifice, wherein a monarch's servants are killed in order for them to continue to serve their master in the next life. Closely related practices found in some tribal societies are cannibalism and headhunting.
Honor killingAn honor killing (American English), honour killing (Commonwealth English), or shame killing is the murder of an individual, either an outsider or a member of a family, by someone seeking to protect what they see as the dignity and honor of themselves or their family. Honor killings are often connected to religion, caste, other forms of hierarchical social stratification, or sexuality. Most often, it involves the murder of a woman or girl by male family members, due to the perpetrators' belief that the victim has brought dishonor or shame upon the family name, reputation or prestige.
GladiatorA gladiator (gladiator, "swordsman", from gladius, "sword") was an armed combatant who entertained audiences in the Roman Republic and Roman Empire in violent confrontations with other gladiators, wild animals, and condemned criminals. Some gladiators were volunteers who risked their lives and their legal and social standing by appearing in the arena. Most were despised as slaves, schooled under harsh conditions, socially marginalized, and segregated even in death.
RomeRome (Italian and Latin: Roma ˈroːma) is the capital city of Italy. It is also the capital of the Lazio region, the centre of the Metropolitan City of Rome, and a special comune named Comune di Roma Capitale. With 2,860,009 residents in , Rome is the country's most populated comune and the third most populous city in the European Union by population within city limits. The Metropolitan City of Rome, with a population of 4,355,725 residents, is the most populous metropolitan city in Italy.
Animal sacrificeAnimal sacrifice is the ritual killing and offering of one or more animals, usually as part of a religious ritual or to appease or maintain favour with a deity. Animal sacrifices were common throughout Europe and the Ancient Near East until the spread of Christianity in Late Antiquity, and continue in some cultures or religions today. Human sacrifice, where it existed, was always much rarer. All or only part of a sacrificial animal may be offered; some cultures, like the ancient and modern Greeks, eat most of the edible parts of the sacrifice in a feast, and burnt the rest as an offering.
DreamA dream is a succession of s, ideas, emotions, and sensations that usually occur involuntarily in the mind during certain stages of sleep. Humans spend about two hours dreaming per night, and each dream lasts around 5 to 20 minutes, although the dreamer may perceive the dream as being much longer than this. The content and function of dreams have been topics of scientific, philosophical and religious interest throughout recorded history.
Narrative poetryNarrative poetry is a form of poetry that tells a story, often using the voices of both a narrator and characters; the entire story is usually written in metered verse. Narrative poems do not need to rhyme. The poems that make up this genre may be short or long, and the story it relates to may be complex. It is normally dramatic, with various characters. Narrative poems include all epic poetry, and the various types of "lay", most ballads, and some idylls, as well as many poems not falling into a distinct type.
Family honorFamily honor (or honour) is an abstract concept involving the perceived quality of worthiness and respectability that affects the social standing and the self-evaluation of a group of related people, both corporately and individually. The family is viewed as the main source of honor, and the community highly values the relationship between honor and the family. The conduct of family members reflects upon family honor and the way the family perceives itself and is perceived by others.
Social influenceSocial influence comprises the ways in which individuals adjust their behavior to meet the demands of a social environment. It takes many forms and can be seen in conformity, socialization, peer pressure, obedience, leadership, persuasion, sales, and marketing. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist Herbert Kelman identified three broad varieties of social influence.
