The locally nilradical for modules over commutative rings
| Title | The locally nilradical for modules over commutative rings |
| Publication Type | Journal Article |
| Year of Publication | 2020 |
| Authors | Kyomuhangi, A, Ssevviiri, D |
| Journal | Contributions to Algebra and Geometry volume |
| Volume | 61 |
| Pagination | 759–769 |
| Date Published | 02 March 2020 |
| Abstract | Let R be a commutative unital ring and a</mi><mo>∈</mo><mi>R</mi><mo>.</mo></math>" id="MathJax-Element-1-Frame" role="presentation" style="box-sizing: inherit; display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" tabindex="0">a∈R.a∈R. We introduce and study properties of a functor a</mi><msub><mi mathvariant="normal">Γ</mi><mrow class="MJX-TeXAtom-ORD"><mi>a</mi></mrow></msub><mo stretchy="false">(</mo><mo>−</mo><mo stretchy="false">)</mo><mo>,</mo></math>" id="MathJax-Element-2-Frame" role="presentation" style="box-sizing: inherit; display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" tabindex="0">aΓa(−),aΓa(−), called the locally nilradical on the category of R-modules. a</mi><msub><mi mathvariant="normal">Γ</mi><mrow class="MJX-TeXAtom-ORD"><mi>a</mi></mrow></msub><mo stretchy="false">(</mo><mo>−</mo><mo stretchy="false">)</mo></math>" id="MathJax-Element-3-Frame" role="presentation" style="box-sizing: inherit; display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" tabindex="0">aΓa(−)aΓa(−) is a generalisation of both the torsion functor (also called section functor) and Baer’s lower nilradical for modules. Several local–global properties of the functor a</mi><msub><mi mathvariant="normal">Γ</mi><mrow class="MJX-TeXAtom-ORD"><mi>a</mi></mrow></msub><mo stretchy="false">(</mo><mo>−</mo><mo stretchy="false">)</mo></math>" id="MathJax-Element-4-Frame" role="presentation" style="box-sizing: inherit; display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" tabindex="0">aΓa(−)aΓa(−) are established. As an application, results about reduced R-modules are obtained and hitherto unknown ring theoretic radicals as well as structural theorems are deduced. |
| URL | https://link.springer.com/article/10.1007/s13366-020-00491-x |