139 research outputs found
Polynomial rings over Goldie-Kerr commutative rings
No full textAll rings in this paper are commutative, and
acc
⊥
\operatorname {acc} \bot
(resp.,
acc
⊕
\operatorname {acc} \, \oplus
) denotes the acc on annihilators (resp., on direct sums of ideals). Any subring of an
acc
⊥
\operatorname {acc} \bot
ring, e.g., of a Noetherian ring, is an
acc
⊥
\operatorname {acc} \bot
ring. Together,
acc
⊥
\operatorname {acc} \bot
and
acc
⊕
\operatorname {acc} \, \oplus
constitute the requirement for a ring to be a Goldie ring. Moreover, a ring
R
R
is Goldie iff its classical quotient ring
Q
Q
is Goldie. A ring
R
R
is a Kerr ring (the appellation is for J. Kerr, who in 1990 constructed the first Goldie rings not Kerr) iff the polynomial ring
R
[
x
]
R[x]
has
acc
⊥
\operatorname {acc} \bot
(in which case
R
R
must have
acc
⊥
\operatorname {acc} \bot
). By the Hilbert Basis theorem, if
S
S
is a Noetherian ring, then so is
S
[
x
]
S[x]
; hence, any subring
R
R
of a Noetherian ring is Kerr. In this note, using results of Levitzki, Herstein, Small, and the author, we show that any Goldie ring
R
R
such that
Q
=
Q
c
(
R
)
Q = {Q_c}(R)
has nil Jacobson radical (equivalently, the nil radical of
R
R
is an intersection of associated prime ideals) is Kerr in a very strong sense:
Q
Q
is Artinian and, hence, Noetherian (Theorems 1.1 and 2.2). As a corollary we prove that any Goldie ring
A
A
that is algebraic over a field
k
k
is Artinian, and, hence, any order
R
R
in
A
A
is a Kerr ring (Theorem 2.5 and Corollary 2.6). The same is true of any algebra
A
A
over a field
k
k
of cardinality exceeding the dimension of
A
A
(Corollary 2.7). Other Kerr rings are: reduced
acc
⊥
\operatorname {acc} \bot
rings and valuation rings with
acc
⊥
\operatorname {acc} \bot
(see 3.3 and 3.4).</p
Progress - The changing times.
No full textInterview with Old Scholar and author Rosemary Hemphill (Goldie) about her memories of St Hilda's
Homomorphisms from functional equations: The Goldie equation, II
No full textThis first of three sequels to Homomorphisms from Functional equations: The Goldie equation (Ostaszewski in Aequationes Math 90:427–448, 2016) by the second author—the second of the resulting quartet—starts from the Goldie functional equation arising in the general regular variation of our joint paper (Bingham et al. in J Math Anal Appl 483:123610, 2020). We extend the work there in two directions. First, we algebraicize the theory, by systematic use of certain groups—the Popa groups arising in earlier work by Popa, and their relatives the Javor groups. Secondly, we extend from the original context on the real line to multi-dimensional (or infinite-dimensional) settings
Goldie Roth unchained: risk and its management in Lian Tanner’s Museum of Thieves
No full textIn her children’s action adventure novel Museum of Thieves, Lian Tanner overtly critiques adult risk-aversion and the over-protection of children. The protagonist is Goldie, an unruly child who escapes the oppressive regime of the City of Jewel where children up to the age of 12 are chained, for their own safety, to adult companions. Goldie escapes Jewel’s power structures and enters a mysterious museum housing the city’s unwanted wildness and danger. In its opening chapter Museum of Thieves establishes a subversive schema that problematises concepts of safety and order and glorifies chaos and risk, but this paper argues that as the novel progresses the author finds the schema increasingly difficult to control. It is tempting to read the museum as a “time out” zone such as CS Lewis’s Narnia, L Frank Baum’s Oz, and Maurice Sendak’s “place where the wild things are”: a space in which child characters can gain self-knowledge and skills before returning to an adult-dominated order. However, because of the degree to which Jewel and its structures are pathologised, Tanner finds she cannot bring Goldie back from “time out”. But rather than being a transgressive text, Museum of Thieves ends in a much less subversive place than it sets out to reach; the museum is revealed as a tightly controlled space and Goldie is well-protected, both within the diegesis by the museum’s special features, and beyond the diegesis by the author and the author’s cognisance of contemporary publishing industry expectations about the depiction of risk in children’s fiction.
Keywords: bubble-wrap; order; chaos; unruly; safety; risk; “time out”; Australian children’s fictio
Homomorphisms from Functional Equations: The Goldie Equation, II
No full textIn this sequel to arXiv1407.4089 by the second author, we extend to
multi-dimensional (or infinite-dimensional) settings the Goldie equation
arising in the general regular variation of `General regular variation, Popa
groups and quantifier weakening', J. Math. Anal. Appl. 483 (2020) 123610, 31
pp. (arXiv1901.05996). We extend the work there in two directions. First, we
algebraicize the theory, by systematic use of certain groups -- the Popa groups
arising in earlier work by Popa, and their relatives the Javor groups.
Secondly, we extend from the original context on the real line to
multi-dimensional (or infinite-dimensional) settings.Comment: Previously titled: Multivariate general regular variation: Popa
groups on vector space
Mountain Bicycles and Their Use in the East Kootenay district, B.C. Provincial Parks
No full textWildland RecreationOff-road bicycle use is a new issue concerning provincial parks. They want to accommodate them, but need to keep conflicts between cyclists and other park trail users, and damage to the environment to a minimum. This report will present a set of recommendations that can be used
PURE CLOSED SUBOBJECTS AND PURE QUOTIENT GOLDIE DIMENSION
No full textWOS: 000464542900004In this note we introduce pure closed subobjects, strongly pure closed subobjects and pure quotient Goldie dimension in finitely accessible additive categories. Then we give a generalization of a classical dimension formula with respect to their pure closed subobjects. We prove that in this category every strongly pure closed subobject of a pure quotient finite dimensional object of every class of objects closed under direct limits and pure epimorphic images has a semilocal endomorphism ring.Scientific and Technological Research Council of TurkeyTurkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) [117F270]; Adnan Menderes University BAPAdnan Menderes University [FEF-17041]The first author is supported by The Scientific and Technological Research Council of Turkey under Grant number 117F270.; Second and third authors are supported by Adnan Menderes University BAP under Grant number FEF-17041
Ta moko: Maori tattoo
No full textThe author examines the history, technique and meaning of ta moko (Maori tattoo) from prehistory to modern times
An analysis of selected periodical articles concerning adult education and the public library, 1958-1967, 1968
No full text- …
