The flat dimension of mixed abelian groups as \(E\)-modules
From MaRDI portal
Publication:1898281
DOI10.1216/rmjm/1181072238zbMath0843.20045OpenAlexW2010222445MaRDI QIDQ1898281
William J. Wickless, H. Pat Goeters, Ulrich F. Albrecht
Publication date: 13 August 1996
Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1216/rmjm/1181072238
endomorphism ringsprojective dimensionmixed Abelian groupsflat dimensionmaximal divisible subgroups\(n\times n\) rational matricesleft \(E\)-modules
Endomorphism rings; matrix rings (16S50) Free, projective, and flat modules and ideals in associative algebras (16D40) Torsion-free groups, infinite rank (20K20) Homological dimension in associative algebras (16E10) Mixed groups (20K21)
Related Items
Homological Properties of Quotient Divisible Abelian Groups ⋮ Fuchs’ problem 34 for mixed Abelian groups ⋮ The quasi-Baer-splitting property for mixed Abelian groups. ⋮ ON A CLASS OF MIXED GROUPS WITH SEMI-LOCAL WALK-ENDOMORPHISM RING ⋮ Realizations of finite dimensional algebras over the rationals ⋮ Direct Sums of Quotient Divisible Groups ⋮ On a theorem of Stelzer for some classes of mixed groups ⋮ SELF-SMALL ABELIAN GROUPS ⋮ Cellular covers of mixed abelian groups ⋮ Subgroups generated by images of endomorphisms of abelian groups and duality ⋮ On the generalized Bassian property for abelian groups ⋮ Unnamed Item ⋮ Direct sums of self-small mixed groups ⋮ Dualities for self–small groups ⋮ Unnamed Item ⋮ Quotient divisible abelian groups ⋮ Cancellation properties for quotient divisible groups. ⋮ Warfield dualities induced by self-small mixed groups ⋮ Modules Over RM-Domains ⋮ Base fields of csp-rings ⋮ On fully idempotent homomorphisms of abelian groups ⋮ A NOTE ON SELF-SMALL MODULES OVER RM-DOMAINS ⋮ Purity and Self-Small Groups ⋮ Quasi-decompositions for Self-Small Abelian Groups ⋮ Self-Small Abelian Groups as Modules over Their Endomorphism Rings ⋮ Fully invariant subgroups, full transitivity, and homomorphism groups of Abelian groups. ⋮ Isomorphisms of endomorphism semigroups of mixed abelian groups ⋮ \(sp\)-groups and their endomorphism rings ⋮ A-Projective Resolutions and an Azumaya Theorem for a Class of Mixed Abelian Groups ⋮ Left comorphic matrix rings ⋮ A-Solvability and Mixed Abelian Groups ⋮ Homomorphisms between A-Projective Abelian Groups and Left Kasch-Rings ⋮ A category of matrices representing two categories of Abelian groups. ⋮ On the Bassian property for abelian groups ⋮ The Baer-Kaplansky theorem for a class of global mixed groups ⋮ A generalization of co-Hopfian abelian groups ⋮ QUASI-ISOMORPHISMS AND GROUPS OF QUASI-HOMOMORPHISMS ⋮ A Note on FinitelyA-Presented Abelian Groups ⋮ Self-small mixed abelian groupsGwithG/T(G) finite rank divisible ⋮ Unnamed Item ⋮ The finite quasi-Baer property.
Cites Work
- Unnamed Item
- Unnamed Item
- Endomorphism rings of faithfully flat Abelian groups
- Abelian groups, \(A\), such that \(\Hom(A,-)\) preserves direct sums of copies of \(A\)
- Primary abelian groups as modules over their endomorphism rings
- On generalized regular rings
- Abelian groups flat as modules over their endomorphism ring
- Examples of torsion-free groups flat as modules over their endomorphism rings
- Faithful Abelian Groups of Infinite Rank
- Regular and principal projective endomorphism rings of mixed abelian groups
- On Locally Free Torsion-Free Rings of Finite Rank
- The endomorphism ring of the additive group of a ring