“Only God Can Be”: Aleksandr Vvedensky, Kant, God, and Time

This article discusses the place of God in the poetic system of Aleksandr Vvedensky. Vvedensky’s famous pronouncement on his “poetic critique” is more throughgoing than Kant’s critical enterprise, and invites a comparison between the movement of Kant’s thought in the Critique of Judgment, and what Vvedensky’s recourse to senselessness aims to achieve. Time in Vvedensky poetics may be seen as a radical extension of Kant’s philosophical system where it ultimately resides in an equally inaccessible realm on which its entire edifice is founded.

Partial actions and cyclic kummer’s theory

We introduce a theory of cyclic Kummer extensions of commutative rings for partial Galois extensions of finite groups, extending some of the well-known results of the theory of Kummer extensions of commutative rings developed by Borevich. In particular, we provide necessary and sufficient conditions to determine when a partial [Formula: see text]-Kummerian extension is equivalent to either a radical or an [Formula: see text]-radical extension, for some subgroup [Formula: see text] of the cyclic group [Formula: see text].

A Counter-Culture of Law: Jurisprudential Change and the Intellectual Origins of the Critical Legal Studies Movement

Critical Legal Studies Movement (CLS) was a critical jurisprudential movement that developed during the 1970s, and came into being in 1977 when the first conference on critical legal studies was held. This article traces the intellectual origins of CLS, providing a comprehensive analysis on its history. The movement was, this article argues, a radical extension of the changes that had occurred in legal scholarship during the 1960s and early 1970s. Moreover, it was a result of a complex mixture of intellectual, scholarly, and political aspects, and it should not be reduced into any one of them.

Graded radicalWtype Lie algebrasI

We get a newℤ-graded Witt type simple Lie algebra using a generalized polynomial ring which is the radical extension of the polynomial ringF[x]with the exponential functionex.

Radical extensions and crossed homomorphisms

If Ω/F is a Galois extension with Galois G and μ(Ω) denotes the group of roots of unity in Ω, we use the group Z1 (G,μ(Ω)) of crossed homomorphisms to study radical extensions inside Ω. Furthermore, we characterise cubic radical extension, and we provide an example to show that this result can not extended for higher degree extensions.

Decidable fragments of field theories

We say φ is an ∀∃ sentence if and only if φ is logically equivalent to a sentence of the form ∀x∃yψ(x, y), where ψ(x, y) is a quantifier-free formula containing no variables except x and y. In this paper we show that there are algorithms to decide whether or not a given ∀∃ sentence is true in (1) an algebraic number field K, (2) a purely transcendental extension of an algebraic number field K, (3) every field with characteristic 0, (4) every algebraic number field, (5) every cyclic (abelian, radical) extension field over Q, and (6) every field.