By Pat Goeters (Editor), Overtoun M.G. Jenda (Editor)
In honor of Edgar Enochs and his venerable contributions to a vast variety of subject matters in Algebra, best researchers from worldwide amassed at Auburn college to document on their most up-to-date paintings and alternate principles on a few of modern-day premier examine themes. This rigorously edited quantity provides the refereed papers of the individuals of those talks in addition to contributions from different veteran researchers who have been not able to attend.
These papers replicate a number of the present issues in Abelian teams, Commutative Algebra, Commutative earrings, crew concept, Homological Algebra, Lie Algebras, and Module concept. available even to starting mathematicians, lots of those articles recommend difficulties and courses for destiny research. This quantity is a phenomenal addition to the literature and a worthy instruction manual for starting in addition to pro researchers in Algebra.
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References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 16 19 20 20 Abstract In this paper, we study an invariant (R) introduced by Scott Chapman to measure how far an HFD R is from being a UFD. We show that if either R contains a prime element or R is a Krull domain with finite divisor class group, then R is a UFD if and only if (R) = 0. However, we give an example of an atomic integral domain R with (R) = 0 which is not an HFD.
3 gives an example of an HFD R which is not a UFD, but (R) = 0. 2 that R conains a prime element is essential. 4 Let K ⊂ F be a proper extension of fields. (a) Let R = K +X F[[X ]]. 3 In particular, R = F2 + X F4 [[X ]] has (R) = 0. (b) Let R = K + X F[X ]. Then R is a one-dimensional HFD, but not a UFD. Note that any f ∈ R with f (0) = 0 is prime in R if and only if it is prime in F[X ]. 2. 2]. Thus (R) = ∞ when F is infinite. In particular, R = R + X C[X ] has (R) = ∞. (c) Let R = F2 + X F4 [X ].
1 1 2 4 5 7 9 10 11 Abstract We survey generalizations of Warfield’s 1968 Homomorphisms and Duality paper. Our main focus is in fixing a module A and examining when Warfield’s results hold relative to this fixed A. 1 Introduction Some of the most promising tools in the study of torsion-free abelian groups and modules have been the ideas developed in Warfield’s paper . Specifically, the Hom/Tensor functors, H om(A, −) / − ⊗ A, and the contravariant functor H om(−, A), referred to as Warfield Duality, where A is a subgroup of the rational integers.
Abelian Groups, Rings, Modules, and Homological Algebra by Pat Goeters (Editor), Overtoun M.G. Jenda (Editor)