$S$-کنش‌های خالص نسبت به ایده‌آل‌های چپ چگال

نویسندگان
مهدیه حدادی
سید مجتبی ناصر شیخ الاسلامی
دانشگاه سمنان
10.52547/mmr.7.3.495
چکیده
در این مقاله قصد داریم مانند آنچه را که لمبک در مورد تعمیم مفهوم زیرمدول‌های خالص با استفاده از یک رادیکال‌ در رسته $R$-مدول‌ها انجام داده است، برای رسته‌ی $S$-کنش‌ها انجام دهیم. به این منظور، ما نوع خاصی از زیرکنش‌های خالص، یعنی زیرکنش‌های $dli$-خالص، که مرتبط با مفهوم رادیکال هونکه است، را در این رسته معرفی می‌کنیم. همچنین نشان می‌دهیم که برای هر رادیکال هونکه

$S$ ،$r$-کنش‌های به طور مطلق $dli$-خالص همان $S$-کنش‌های $r$-انژکتیو ضعیف هستند. سپس به وسیله‌ی هر ایده‌آل چپ $r$-چگال، عملگر بستاری را معرفی می‌کنیم که ارتباط نزدیکی با مفهوم $S$-کنش‌های $dli$-خالص دارد. سپس این ارتباط را به‌ طور مفصل مورد بررسی قرار می‌دهیم.
کلیدواژه‌ها
S-کنش
رادیکال
ایده‌آل r-چگال
زیرکنش dli-خالص

عنوان مقاله English

On dense left ideal pure $S$-acts

نویسندگان English

mahdieh Haddadi
seyed mojtaba naser Sheykholislami
Semnan University
چکیده English

In this paper, similar to the Lembek's idea concerning a generalization of the notion of purity associated with a radical in the category of R-modules, we give the notion of purity related to a Hoehnke radical, d.l.i.pure, in the category of $S$-acts and investigate this notion. We also show that absolutely d.l.i.pure $S$-acts are exactly the $r$-weakly injective $S$-acts, for every Hoehnke radical $r$, and we give several characterization of d.l.ipure $S$-acts. We then present a closure operator induced by an $r$-dense left ideal which is closely related to the notion of d.l.i.purity and give a characterization of d.l.i.pure $S$-acts by this closure operator.

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کلیدواژه‌ها English

$S$-act
radical
$r$-dense
d.l.i.pure
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