Generalized π-Baer *-rings | ||
| Journal of Algebraic Systems | ||
| دوره 12، شماره 2، فروردین 2025، صفحه 347-366 اصل مقاله (203.75 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2023.12507.1670 | ||
| نویسندگان | ||
| Ali Shahidikia1؛ Haimd Haj Seyyed Javadi* 2 | ||
| 1Department of Mathematics, Dezful Branch, Islamic Azad University, Dezful, Iran. | ||
| 2Department of Computer Engineering, Shahed University, Tehran, Iran. | ||
| چکیده | ||
| A *-ring $R$ is called a generalized $\pi$-Baer *-ring, if for any projection invariant left ideal $Y$ of $R$, the right annihilator of $Y^n$ is generated, as a right ideal, by a projection, for some positive integer $n$, depending on $Y$. In this paper, we study some properties of generalized $\pi$-Baer *-rings. We show that this notion is well-behaved with respect to polynomial extensions, full matrix rings, and several classes of triangular matrix rings. We indicate interrelationships between the generalized $\pi$-Baer *-rings and related classes of rings such as generalized $\pi$-Baer rings, generalized Baer *-rings, generalized quasi-Baer *-rings, and $\pi$-Baer \s-rings. We obtain algebraic examples which are generalized $\pi$-Baer $ \ast $-rings but are not $\pi$-Baer *-rings. We show that for pre-C*-algebras these two notions are equivalent. We obtain classes of Banach *-algebras which are generalized $\pi$-Baer *-rings but are not $\pi$-Baer *-rings. We finish the paper by showing that for a locally compact abelian group $G$, the group algebra $L^{1}(G)$ is a generalized $\pi$-Baer $*$-ring, if and only if so is the group C*-algebra $C^{*}(G)$, if and only if $G$ is finite. | ||
| کلیدواژهها | ||
| generalized π-Baer ring؛ generalized π-Baer ∗-ring؛ generalized quasi-Baer ∗-ring؛ generalized Baer ring؛ generalized Baer ∗-ring | ||
| مراجع | ||
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