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Everything about Perfect ring
In the area of abstract algebra known as ring theory, a left perfect ring is a type of ring over which all left modules have projective covers. The right case is defined by analogy, and the condition is not left-right symmetric; that is, there exist rings which are perfect on one side but not the other. Perfect rings were introduced in Bass's book. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Perfect ringA 5-minute orientation
- Skim a recent paper: Understanding, quantifying, and controlling the molecular ordering of semiconducting polymers: from novices to experts and amorphous to perfect crystalsInfluential work since 2022
- Pick up a classic book: British Social Wasps: An Introduction to Their Anatomy and Physiology ...The most-reprinted book on the subject
- Read the landmark paper: “Perfect” designer chromosome V and behavior of a ring derivativeCited 225 times
- Go sideways: Glossary of module theoryA closely related topic
- Go sideways: Decomposition of a moduleA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
“Perfect” designer chromosome V and behavior of a ring derivative
Perfect metamaterial absorber based on a split-ring-cross resonator
Thermally robust ring‐shaped chromium perfect absorber of visible light
Vaginal Ring Adherence in Sub-Saharan Africa: Expulsion, Removal, and Perfect Use
Reconfigurable generation of double-ring perfect vortex beam
High-speed gate-tunable terahertz coherent perfect absorption using a split-ring graphene
Tunable terahertz perfect absorber with a graphene-based double split-ring structure
Monte Carlo study of freely jointed ring polymers. III. The generation of undistorted perfect ring polymers
🆕 Influential since 2022
Understanding, quantifying, and controlling the molecular ordering of semiconducting polymers: from novices to experts and amorphous to perfect crystals
Terahertz narrowband perfect metasurface absorber based on micro-ring-shaped GaAs array for enhanced refractive index sensing
An ultra-broadband near-perfect solar absorber based on monolayer MoS2 with titanium ring-pillar arrays
Polarization Insensitive Circular Ring Resonator Based Perfect Metamaterial Absorber Design and Simulation on a Silicon Substrate
Quad-Band Metamaterial Perfect Absorber with High Shielding Effectiveness Using Double X-Shaped Ring Resonator
📚 Books worth reading
British Social Wasps: An Introduction to Their Anatomy and Physiology ...Edward Latham Ormerod , BookLab (Firm) · 1868- 📕Topology and geometry in dimension threeWilliam H. Jaco · 2011
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Glossary of module theory Module theory is the branch of mathematics in which modules are studied. This is a glossary of some terms of the subject. See also: Glossary of linear…
- Decomposition of a module In abstract algebra, a decomposition of a module is a way to write a module as a direct sum of modules. A type of a decomposition is often used to define…
- Projective cover In the branch of abstract mathematics called category theory, a projective cover of an object M is in a sense the best approximation of M by a projective…
- Idempotent (ring theory) In ring theory, a branch of mathematics, an idempotent element or simply idempotent of a ring is an element a such that a2 = a. That is, the element is…
- Morita equivalence In abstract algebra, Morita equivalence is a relationship defined between rings that preserves many ring-theoretic properties. More precisely, two rings…
- Glossary of ring theory Ring theory is the branch of mathematics in which rings are studied: that is, structures supporting both an addition and a multiplication operation. This…
- Quasi-Frobenius ring In mathematics, especially ring theory, the class of Frobenius rings and their generalizations are the extension of work done on Frobenius algebras. Perhaps…
- 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…