Rings Over Which Cyclics are Direct Sums of Projective and CS or Noetherian

R is called a right WV -ring if each simple right R-module is injective relative to proper cyclics. If R is a right WV -ring, then R is right uniform or a right V -ring. It is shown that for a right WV-ring R, R is right noetherian if and only if each right cyclic module is a direct sum of a projective module and a CS or noetherian module. For a finitely generated module M with projective socle over a V -ring R such that every subfactor of M is a direct sum of a projective module and a CS or noetherian module, we show M = X \oplus T, where X is semisimple and T is noetherian with zero socle. In the case that M = R, we get R = S \oplus T, where S is a semisimple artinian ring, and T is a direct sum of right noetherian simple rings with zero socle. In addition, if R is a von Neumann regular ring, then it is semisimple artinian.Comment: A Para\^itre Glasgow Mathematical Journa

The BTC40 Survey for Quasars at 4.8 < z < 6

The BTC40 Survey for high-redshift quasars is a multicolor search using images obtained with the Big Throughput Camera (BTC) on the CTIO 4-m telescope in V, I, and z filters to search for quasars at redshifts of 4.8 < z < 6. The survey covers 40 sq. deg. in B, V, & I and 36 sq. deg. in z. Limiting magnitudes (3 sigma) reach to V = 24.6, I = 22.9 and z = 22.9. We used the (V-I) vs. (I-z) two-color diagram to select high-redshift quasar candidates from the objects classified as point sources in the imaging data. Follow-up spectroscopy with the AAT and CTIO 4-m telescopes of candidates having I < 21.5 has yielded two quasars with redshifts of z = 4.6 and z = 4.8 as well as four emission line galaxies with z = 0.6. Fainter candidates have been identified down to I = 22 for future spectroscopy on 8-m class telescopes.Comment: 27 pages, 8 figures; Accepted for publication in the Astronomical Journa

Some rings for which the cosingular submodule of every module is a direct summand

The submodule Z(M) = ∩{N | M/N is small in its injective hull} was introduced by Talebi and Vanaja in 2002. A ring R is said to have property (P ) if Z(M) is a direct summand of M for every R-module M . It is shown that a commutative perfect ring R has (P ) if and only if R is semisimple. An example is given to show that this characterization is not true for noncommutative rings. We prove that if R is a commutative ring such that the class {M ∈ Mod−R | ZR(M) = 0} is closed under factor modules, then R has (P ) if and only if the ring R is von Neumann regular

Recent Decisions

Comments on recent decisions by William C. Rindone, Ray F. Drexler, Eugene G. Griffin, Ronald Patrick Smith, and John G. Curran