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Abstract
In a previous work [3], the current author, together with P. R. Hall, studied various kinds of primeness in near-rings and sandwich near-rings of continuous functions. In this paper, we study various prime radicals for sandwich near-rings. In certain cases, complete characterisations of the prime, 3-prime, equiprime and strongly equiprime radicals are obtained.
The Brown-McCoy radical
is known to be an ideal-hereditary Kurosh-Amitsur radical in the variety of zerosymmetric near-rings. We define the Brown-McCoy and simplical radicals,
and
, respectively, for zerosymmetric Γ-near-rings. Both
and
are ideal-hereditary Kurosh-Amitsur radicals in that variety. IfM is a zerosymmetric Γ-near-ring with left operator near-ringL, it is shown that
, with equality ifM has a strong left unity.
is extended to the variety of arbitrary near-rings, and
and
are extended to the variety of arbitrary Γ-near-rings, in a way that they remain Kurosh-Amitsur radicals. IfN is a near-ring andA ⊲N, then
, with equality ifA if left invariant.
Summary
We continue our study of the lattice of matric-extensible radicals of associative rings. We find some atoms generated by simple rings of the lattices of all matric-extensible radicals, matric-extensible supernilpotent radicals and matric-extensible special radicals. We consider *-rings, which were previously defined by the second author, and consider when they generate atoms of these lattices.
It was previously shown that every special radical classR of rings induces a special radical class ?R of G-rings. Amongst the special radical classes of near-rings, there are some, called the s-special radical classes, which induce, special radical classes of G-near-rings by the same procedure as used in the ring case. The s-special radicals of near-rings possess very strong hereditary properties. In particular, this leads to some new results for the equiprime andI 3 radicals.
Abstract
A class K of rings has the GADS property (i.e., generalized ADS property) if wheneverX& I& R with X∈ K , then there exists B & R with B ∈ K such that X ⊆ B ⊆ I. Radicals whose semisimple classes have the GADS property are called g-radicals. In this paper, we fully characterize the class of g -radicals. We show that ? is a g-radical if and only if either ? ⊆ I or S ? ⊆ I , where I denotes the class of idempotent rings and S ? denotes the semisimple class of ?. It is also shown that the (hereditary) g-radicals form an (atomic) sublattice of the lattice of all radicals.
Abstract
A series of fluoropolymer films was synthesized by reacting 1,3-bis(1,1,1,3,3,3-hexafluoro-2-pentafluorophenylmethoxy-2-propyl)benzene (12F-FBE) with a series of bisphenol monomers via a polycondensation reaction. The biphenols used included a diphenol-substituted spirodilactam, biphenol, bisphenol A, bisphenol AF, bisphenol F and bisphenol O. Polymers films from these new fluoropolyaryl ethers were irradiated by a Gamma Beam 657-PT at a dose rate of 9 kGy/h; the absorbed dose was varied between 30 and 150 kGy. The effect on the chemical structure upon radiation was studied by DSC, TGA, FTIR-ATR, NMR, and GPC, both before and after irradiation. The data obtained allowed the determination of the degradation radiochemical yield (G s), between 0.24 and 7.43 crosslinking radiochemical yield (G x), from 0.03 to 1.47 and the ratio of G s/G x was between 2.89 and 8.28. There was no apparent physical change, from 30 to 150 kGy; the films continue to be flexible and transparent after irradiation.
Summary
Heat and CO2rates are measured on M. domesticapupae as a function of age and temperature. Heats of combustion of flies, pupae, and puparia are also measured. Heat and CO2rates decrease for 3 d post-pupation and increase exponentially over 4 d prior to eclosure. Heat and CO2rates are low and increase slowly from 5 to 23C, then rapidly increase from 23 to 26C, then more slowly up to 38C where pupae are stressed. Respiratory substrate varies with age and temperature, is a mix of lipids and carbohydrates, and has an average carbon oxidation state of -0.3 at room temperature. Humidity, elevated CO2, or reduced O2did not affect pupal metabolism.
