When some complement of an exact submodule is a direct summand

2021 ◽  
pp. 1-13
Author(s):  
Adnan Tercan ◽  
Ramazan Yaşar
Keyword(s):  
Direct Summand

Relative characters for H-projective RG-lattices

1988 ◽  
Vol 104 (2) ◽  
pp. 207-213 ◽  
Author(s):  
Peter Symonds
Keyword(s):  
Representation Theory ◽  
Direct Summand ◽  
Modular Representation ◽  
Dedekind Domain ◽  
Modular Representation Theory ◽  
Trivial Group ◽  
Ordinary Character ◽  
Projective Lattices

If G is a group with a subgroup H and R is a Dedekind domain, then an H-projective RG-lattice is an RG-lattice that is a direct summand of an induced lattice for some RH-lattice N: they have been studied extensively in the context of modular representation theory. If H is the trivial group these are the projective lattices. We define a relative character χG/H on H-projective lattices, which in the case H = 1 is equivalent to the Hattori–Stallings trace for projective lattices (see [5, 8]), and in the case H = G is the ordinary character. These characters can be used to show that the R-ranks of certain H-projective lattices must be divisible by some specified number, generalizing some well-known results: cf. Corollary 3·6. If for example we take R = ℤ, then |G/H| divides the ℤ-rank of any H-projective ℤG-lattice.

A GENERALIZATION OF SEMISIMPLE ARTINIAN RINGS

2005 ◽  
Vol 04 (03) ◽  
pp. 231-235
Author(s):  
YASUYUKI HIRANO ◽  
HISAYA TSUTSUI
Keyword(s):  
Direct Summand ◽  
Artinian Rings

We investigate a ring R with the property that for every right R-module M and every ideal I of R the annihilator of I in M is a direct summand of M, and determine conditions under which such a ring is semisimple Artinian.

scholarly journals Almost direct summands

2014 ◽  
Vol 214 ◽  
pp. 195-204 ◽  
Author(s):  
Bhargav Bhatt
Keyword(s):  
Direct Summand ◽  
Hodge Theory ◽  
Fundamental Theorems ◽  
Ramification Locus

AbstractWe prove new cases of the direct summand conjecture using fundamental theorems inp-adic Hodge theory due to Faltings. The cases tackled include the ones when the ramification locus lies entirely in characteristicp.

Semiregular Modules and Rings

1976 ◽  
Vol 28 (5) ◽  
pp. 1105-1120 ◽  
Author(s):  
W. K. Nicholson
Keyword(s):  
Direct Summand ◽  
Homomorphic Image ◽  
Projective Module ◽  
Structure Theorem ◽  
Projective Cover ◽  
Finitely Generated

Mares [9] has called a projective module semiperfect if every homomorphic image has a projective cover and has shown that many of the properties of semiperfect rings can be extended to these modules. More recently Zelmanowitz [16] has called a module regular if every finitely generated submodule is a projective direct summand. In the present paper a class of semiregular modules is introduced which contains all regular and all semiperfect modules. Several characterizations of these modules are given and a structure theorem is proved. In addition several theorems about regular and semiperfect modules are extended.

scholarly journals On a class of dual Rickart modules

2020 ◽  
Vol 72 (7) ◽  
pp. 960-970
Author(s):  
R. Tribak
Keyword(s):  
Direct Summand ◽  
Noetherian Ring ◽  
Commutative Noetherian Ring ◽  
Direct Sum ◽  
Finite Set ◽  
Rickart Modules

UDC 512.5 Let R be a ring and let Ω R be the set of maximal right ideals of R . An R -module M is called an sd-Rickart module if for every nonzero endomorphism f of M , ℑ f is a fully invariant direct summand of M . We obtain a characterization for an arbitrary direct sum of sd-Rickart modules to be sd-Rickart. We also obtain a decomposition of an sd-Rickart R -module M , provided R is a commutative noetherian ring and A s s ( M ) ∩ Ω R is a finite set. In addition, we introduce and study ageneralization of sd-Rickart modules.

A Direct Summand in H ∗ (MO 〈8 〉, Z 2 )

1980 ◽  
Vol 78 (2) ◽  
pp. 295 ◽  
Author(s):  
A. P. Bahri ◽  
M. E. Mahowald
Keyword(s):  
Direct Summand

scholarly journals Representations of quadratic forms

1978 ◽  
Vol 69 ◽  
pp. 117-120
Author(s):  
Yoshiyuki Kitaoka
Keyword(s):  
Direct Summand ◽  
Quadratic Forms ◽  
Quadratic Space ◽  
List Type

We have shown in [1]Theorem A. Let L be a lattice in a regular quadratic space U over Q; then L has a submodule M satisfying the following conditions 1),2): 1)dM ≠ 0, rank M = rank L — 1, and M is a direct summand of L as a module.2)Let L′ be a lattice in some regular quadratic space U′ over Q satisfying dL′ = dL, rank L′ — rank L, tp(L′) ≥ tp(L) for any prime p. If there is an isometry α from M into L′ such that α(M) is a direct summand of L′ as a module, then L′ is isometric to L.

ABELIAN GROUPS WITH THE DIRECT SUMMAND SUM PROPERTY

2002 ◽  
Vol 35 (3) ◽  
pp. 477-492
Author(s):  
Dumitru Vălcan
Keyword(s):  
Direct Summand ◽  
Abelian Groups
Sign in / Sign up

Export Citation Format

Share Document