By Pat Goeters (Editor), Overtoun M.G. Jenda (Editor)

In honor of Edgar Enochs and his venerable contributions to a vast variety of issues in Algebra, best researchers from all over the world accrued at Auburn collage to document on their most recent paintings and alternate principles on a few of cutting-edge most popular learn subject matters. This conscientiously edited quantity provides the refereed papers of the members of those talks besides contributions from different veteran researchers who have been not able to attend.

These papers mirror a few of the present issues in Abelian teams, Commutative Algebra, Commutative jewelry, crew conception, Homological Algebra, Lie Algebras, and Module conception. obtainable even to starting mathematicians, lots of those articles recommend difficulties and courses for destiny examine. This quantity is an exceptional addition to the literature and a priceless instruction manual for starting in addition to professional researchers in Algebra.

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**Additional resources for Abelian Groups, Rings, Modules, and Homological Algebra**

**Example text**

If A is slender, then direct summands of A I are A-reflexive as long as I has non-measurable cardinality. In general, A-reflexive modules have a zero A-radical. An exact sequence 0 → B → C → M → 0 of right R-modules is A-cobalanced if the induced sequence 0 → M ∗ → C ∗ → B ∗ → 0 of left E-modules is exact. 1 ([4]) Let A be a slender R-module of non-measurable cardinality. The following are equivalent for a right R-module M of non-measurable cardinality: a) M is A-reflexive. b) There exists an A-cobalanced sequence 0 → M → A I → N → 0 with R A (N ) = 0 and |I | non-measurable.

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 [49]. 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.

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 [49]. 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.