Jacobson Radical Theory

Author(s):  
T. Y. Lam
Author(s):  
Puguh Wahyu Prasetyo

The development of Ring Theory motivates the existence of the development of the Radical Theory of Rings. This condition is motivated since there are rings which have properties other than those owned by the set ring of all integers. These rings are collected so that they fulfill certain properties and they are called radical classes of rings. As the development of science about how to separate the properties of radical classes of rings motivates the existence of supernilpotent radical classes. On the other hand, there exists the concept of graded rings. This concept can be generalized into the Radical Theory of Rings. Thus, the properties of the graded supernilpotent radical classes are very interesting to investigate. In this paper, some graded supernilpotent radical of rings are given and their construction will be described. It follows from this construction that the graded Jacobson radical is a graded supernilpotent radical.


2020 ◽  
Vol 22 (2) ◽  
pp. 175-187
Author(s):  
Herman Westerink ◽  
Philippe Van Haute

Although Freud's ‘Family Romances’ from 1909 is hardly ever discussed at length in secondary literature, this article highlights this short essay as an important and informative text about Freud's changing perspectives on sexuality in the period in which the text was written. Given the fact that Freud, in his 1905 Three Essays, develops a radical theory of infantile sexuality as polymorphously perverse and as autoerotic pleasure, we argue that ‘Family Romances’, together with the closely related essay on infantile sexual theories (1908), paves the way for new theories of sexuality defined in terms of object relations informed by knowledge of sexual difference. ‘Family Romances’, in other words, preludes the introduction of the Oedipus complex, but also – interestingly – gives room for a Jungian view of sexuality and sexual phantasy. ‘Family Romances’ is thus a good illustration of the complex way in which Freud's theories of sexuality developed through time.


Author(s):  
Galen Strawson

This chapter argues that the unqualified attribution of the radical theory to John Locke is mistaken if we are to take into account the fact that the theory allows for freaks like [Sₓ]. It first considers [I]-transfer without [P]-transfer—that is, [I]-transfer preserving personal identity—before discussing Locke's response to the idea that personal identity might survive [I]-transfer from an a priori point of view. It suggests that [I]-transfer is possible in such a way that the existence of a single Person [P₁] from t₁ to t₂ can successively (and non-overlappingly) involve the existence of two immaterial substances. It also explains how Locke's claim that [I]-transfer is possible opens up the possibility that it could go wrong, in such a way as to lead to injustice. Finally, it examines Locke's notion of “sensible creature,” which refers to a subject of experience who is a person.


1986 ◽  
Vol 48 ◽  
pp. 13-13
Author(s):  
George Galster

The following note describes a skit designed primarily as a pedagogic device to illustrate in a meaningful (and, hopefully, provocative and humorous) way Marx's analysis of capitalism. Numerous concepts and phenomena are “brought to life” in the skit: exploitation, immiseration and alienation of workers, maintenance wage, labor theory of value, mechanization and the division of labor, systemic tendencies toward economic crises, relationship of various superstructural components (welfare, religion, etc.) to the economic base, and the radical theory of the state. More specifically, the economic base of a hypothetical capitalist society consists of a stylized production process involving “resources” (Oreo cookies), “labor” (students selected from the class) and eventually “capital” (table knives). The ability of the monopoly capitalist to accumulate surplus by exploiting workers becomes manifest. Other elements of the social superstructure (unions, government, religion, etc.)


2019 ◽  
Vol 23 (1) ◽  
pp. 265-273
Author(s):  
Eckhard Lobsien

Abstract What sort of object is a literary text? From a phenomenological point of view - phenomenology considered as both a radical theory of reading and a theory of radical reading - a range of answers arise, many of them tinged with deconstructive momentum. This paper aims at pointing out some basic issues in reading literary texts, offering ten theses on the enduring tasks of phenomenological literary theory.


Author(s):  
Ravi Srinivasa Rao ◽  
K. Siva Prasad ◽  
T. Srinivas

By a near-ring we mean a right near-ring.J0r, the right Jacobson radical of type 0, was introduced for near-rings by the first and second authors. In this paper properties of the radicalJ0rare studied. It is shown thatJ0ris a Kurosh-Amitsur radical (KA-radical) in the variety of all near-ringsR, in which the constant partRcofRis an ideal ofR. So unlike the left Jacobson radicals of types 0 and 1 of near-rings,J0ris a KA-radical in the class of all zero-symmetric near-rings.J0ris nots-hereditary and hence not an ideal-hereditary radical in the class of all zero-symmetric near-rings.


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