Live briefing
Everything about Simple ring
Type of ring in non-commutative algebra
In mathematics, a simple ring is a non-zero ring that has no two-sided ideals besides the zero ideal and itself. In particular, a commutative ring is a simple ring if and only if it is a field. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Simple ringA 5-minute orientation
- Skim a recent paper: A green and sensitive guanine-based DNA biosensor for idarubicin anticancer monitoring in biological samples: A simple and fast strategy for control of health quality in chemotherapy procedure confirmed by docking investigationInfluential work since 2022
- Pick up a classic book: Dualities and Representations of Lie Superalgebras (Graduate Studies in Mathematics)The most-reprinted book on the subject
- Read the landmark paper: Predicting species distribution: offering more than simple habitat modelsCited 5,513 times
- Go sideways: Noncommutative ringA closely related topic
- Go sideways: Wedderburn–Artin theoremA closely related topic
📖 Definitions
Noun A ring that contains no nontrivial ideals (i.e., no (two-sided) ideals other than the zero ideal and the ring itself).
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Predicting species distribution: offering more than simple habitat models
A Simple and General Method for Transferring Genes into Plants
A rapid and simple method for measuring thymocyte apoptosis by propidium iodide staining and flow cytometry
BLAST Ring Image Generator (BRIG): simple prokaryote genome comparisons
An example of a simple radical ring
A SIMPLE NIL RING EXISTS
Ring of simple polytopes and differential equations
A simple universal property of Thom ring spectra
🆕 Influential since 2022
A green and sensitive guanine-based DNA biosensor for idarubicin anticancer monitoring in biological samples: A simple and fast strategy for control of health quality in chemotherapy procedure confirmed by docking investigation
Simple Contrastive Graph Clustering
A Simple, Selective, and General Catalyst for Ring Closing Depolymerization of Polyesters and Polycarbonates for Chemical Recycling
A Simple Nonfused Ring Electron Acceptor with a Power Conversion Efficiency Over 16%†
Simple non-fused ring electron acceptors with well-controlled terminal group stacking
📚 Books worth reading
Dualities and Representations of Lie Superalgebras (Graduate Studies in Mathematics)Shun-jen Cheng, Weiqiang Wang · 2012- 📕Lie algebras and related topicsHelmut Strade, Marina Avitabile · 2015
- 📕Lie superalgebras and enveloping algebrasIan M. Musson · 2012
- 📕Unipotent and nilpotent classes in simple algebraic groups and lie algebrasM. W. Liebeck · 2012
- 📕Classification and identification of Lie algebrasLibor Snobl · 2014
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Noncommutative ring In mathematics, a noncommutative ring is a ring whose multiplication is not commutative; that is, there exist a and b in the ring such that ab and ba are…
- Wedderburn–Artin theorem In algebra, the Wedderburn–Artin theorem is a classification theorem for semisimple rings and semisimple algebras. The theorem states that a(n Artinian)…
- Matrix ring In abstract algebra, a matrix ring is a set of matrices with entries in a ring R that form a ring under matrix addition and matrix multiplication. The…
- Semisimple module In mathematics, especially in the area of abstract algebra known as module theory, a semisimple module or completely reducible module is a type of module…
- Semisimple algebra In ring theory, a branch of mathematics, a semisimple algebra is an associative Artinian algebra over a field which has trivial Jacobson radical (only…
- Artinian ring In mathematics, specifically abstract algebra, an Artinian ring (sometimes Artin ring) is a ring that satisfies the descending chain condition on (one-sided)…
- Central simple algebra In ring theory and related areas of mathematics a central simple algebra (CSA) over a field K is a finite-dimensional associative K-algebra A that is simple…
- Division ring In algebra, a division ring, also called a skew field, is a nontrivial ring in which division by nonzero elements is defined. Specifically, it is a nontrivial…