Kernel-endoregular modules and the morphic property
This paper describes properties of three certain classes of modules M over a ring R determined by conditions on isomorphic direct summands ( ≲ ⊕ ): The condition that whenever ( I m λ ≅ ) M / Ker λ ≲ ⊕ M then Ker λ and I m λ are direct summands of M for any endomorphism λ ∈ End ( M ) (kernel-endoreg...
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| Veröffentlicht in: | Communications in algebra Jg. 52; H. 5; S. 1818 - 1825 |
|---|---|
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| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Abingdon
Taylor & Francis
03.05.2024
Taylor & Francis Ltd |
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| ISSN: | 0092-7872, 1532-4125 |
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| Abstract | This paper describes properties of three certain classes of modules M over a ring R determined by conditions on isomorphic direct summands (
≲
⊕
):
The condition that whenever
(
I
m
λ
≅
)
M
/
Ker
λ
≲
⊕
M
then
Ker
λ
and
I
m
λ
are direct summands of M for any endomorphism
λ
∈
End
(
M
)
(kernel-endoregular modules).
The condition that if
M
/
A
≅
B
where A,
B
≲
⊕
M
then
M
/
B
≅
A
(iso-summand-morphic modules).
The condition if
M
/
A
≅
B
where A,
B
≤
⊕
M
, then
M
/
B
≅
A
(summand-morphic modules) which is precisely the internal cancellation property for modules. |
|---|---|
| AbstractList | This paper describes properties of three certain classes of modules M over a ring R determined by conditions on isomorphic direct summands (≲⊕):The condition that whenever (Imλ≅)M/Kerλ≲⊕M then Kerλ and Imλ are direct summands of M for any endomorphism λ∈End(M) (kernel-endoregular modules).The condition that if M/A≅B where A, B≲⊕M then M/B≅A (iso-summand-morphic modules).The condition if M/A≅B where A, B≤⊕M, then M/B≅A (summand-morphic modules) which is precisely the internal cancellation property for modules. This paper describes properties of three certain classes of modules M over a ring R determined by conditions on isomorphic direct summands ( ≲ ⊕ ): The condition that whenever ( I m λ ≅ ) M / Ker λ ≲ ⊕ M then Ker λ and I m λ are direct summands of M for any endomorphism λ ∈ End ( M ) (kernel-endoregular modules). The condition that if M / A ≅ B where A, B ≲ ⊕ M then M / B ≅ A (iso-summand-morphic modules). The condition if M / A ≅ B where A, B ≤ ⊕ M , then M / B ≅ A (summand-morphic modules) which is precisely the internal cancellation property for modules. |
| Author | Koşan, M. Tamer Taşdemir, Özgür |
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| References | e_1_3_2_16_1 e_1_3_2_9_1 e_1_3_2_8_1 e_1_3_2_18_1 e_1_3_2_7_1 Clark J. (e_1_3_2_6_1) 2006 Oshiro K. (e_1_3_2_17_1) 1983; 20 e_1_3_2_10_1 e_1_3_2_11_1 Aydogdu P. (e_1_3_2_2_1) 2008; 10 e_1_3_2_5_1 e_1_3_2_4_1 e_1_3_2_14_1 e_1_3_2_3_1 e_1_3_2_15_1 Hamdouni A. (e_1_3_2_13_1) 2005; 5 Hai P. T. (e_1_3_2_12_1) 2020; 57 |
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| Snippet | This paper describes properties of three certain classes of modules M over a ring R determined by conditions on isomorphic direct summands (
≲
⊕
):
The... This paper describes properties of three certain classes of modules M over a ring R determined by conditions on isomorphic direct summands (≲⊕):The condition... |
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| SubjectTerms | (co-)Hopfian module (dual-)Rickart module C2 modules D2 modules endoregular module Modules morphic module Primary: 16D10 unit-regular module |
| Title | Kernel-endoregular modules and the morphic property |
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