| Autor: |
Quynh, T. C., Abyzov, A., Koşan, M. T. |
| Zdroj: |
Lobachevskii Journal of Mathematics; Dec2019, Vol. 40 Issue 12, p2103-2110, 8p |
| Abstrakt: |
We introduce a symmetry property for unit-regular rings as follows: a ∈ R is unit-regular if and only if aR ⊕ (a − u)R = R (equivalently, Ra ⊕ R(a − u) = R) for some unit u of R if and only if aR ⊕ (a − u)R =(2a − u)R (equivalently, Ra ⊕ R(a − u) = R(2a − u)) for some unit u of R. Let M and N be right R-modules and α, β ∈ Hom(M, N) such that α + β is regular. It is shown that αS ⊕ βS =(α + β)S, where S = End(M) if and only if Tα ⊕ Tβ = T(α + β), where T = End(N). We also introduce partial order α ≤⊕β and minus partial order α ≤−β for any α, β ∈ Hom(M, N); they translate into module-theoretic language defined in a ring in [7] and [8]. We analyze some relationships between ≤⊕ and ≤− on the endomorphism rings of the modules M and N. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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