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Everything about Prime element
Analogue of a prime number in a commutative ring
In mathematics, specifically in abstract algebra, a prime element of a commutative ring is an object satisfying certain properties similar to the prime numbers in the integers and to irreducible polynomials. Care should be taken to distinguish prime elements from irreducible elements, a concept that is the same in unique factorization domains but not the same in general. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Prime elementA 5-minute orientation
- Skim a recent paper: Evaluate All The Order of Every Element in The Higher Even, Odd, and Prime Order of Group for CompositionInfluential work since 2022
- Pick up a classic book: Noncommutative rings and their applicationsThe most-reprinted book on the subject
- Read the landmark paper: Simple Combinations of Lineage-Determining Transcription Factors Prime cis-Regulatory Elements Required for Macrophage and B Cell IdentitiesCited 13,963 times
- Go sideways: Integral domainA closely related topic
- Go sideways: Unique factorization domainA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Simple Combinations of Lineage-Determining Transcription Factors Prime cis-Regulatory Elements Required for Macrophage and B Cell Identities
Finite Groups in Which Every Element Has Prime Power Order
Recognition of alternating groups of prime degree from their element orders
Primitive Permutation Groups Containing an Element of Large Prime Order
Finite soluble groups containing an element of prime order whose centralizer is small
PERIODIC LOCALLY SOLUBLE GROUPS CONTAINING AN ELEMENT OF PRIME ORDER WITH ČERNIKOV CENTRALIZER
HOW FAR IS AN ELEMENT FROM BEING PRIME?
Finite Element Evaluation of Vertical Bearing Capacity Factors $$N_{c}^{\prime }$$ N c ′ , $$N_{q}^{\prime }$$ N q ′ and $$N_{\gamma }^{\prime }$$ N γ ′ for Ring Footings
🆕 Influential since 2022
Evaluate All The Order of Every Element in The Higher Even, Odd, and Prime Order of Group for Composition
Computation of plane potential flow around multi-element airfoils using the Schottky–Klein prime function
On groups in which every element has a prime power order and which satisfy some boundedness condition
Fifth Element and Prime Mover
Prime order element graph of a group
📚 Books worth reading
- 📕Noncommutative rings and their applicationsFrance) International Conference on Noncommutative Rings and Their Applications (2013 Artois · 2015
- 📕Si ku ti yao zhu lu cong shuXuan Zheng, Dong Hui · 2010
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Integral domain In mathematics, an integral domain is a nonzero commutative ring in which the product of any two nonzero elements is nonzero. In an integral domain, every…
- Unique factorization domain In mathematics, a unique factorization domain (UFD) (also sometimes called a factorial ring following the terminology of Bourbaki) is a ring in which a…
- Principal ideal domain In mathematics, a principal ideal domain, or PID, is an integral domain (that is, a non-zero commutative ring without nonzero zero divisors) in which every…
- Prime ideal In algebra, a prime ideal is a subset of a ring that shares many important properties of a prime number in the ring of integers. The prime ideals for the…
- Gauss's lemma (polynomials) In algebra, Gauss's lemma, named after Carl Friedrich Gauss, is a theorem about polynomials over the integers, or, more generally, over a unique factorization…
- Polynomial ring In mathematics, especially in the field of algebra, a polynomial ring or polynomial algebra is a ring formed from the set of polynomials in one or more…
- Irreducible polynomial In mathematics, an irreducible polynomial is, roughly speaking, a polynomial that cannot be factored into the product of two non-constant polynomials.…
- Irreducible element In algebra, an irreducible element of an integral domain is a non-zero element that is not invertible (that is, is not a unit), and is not the product…