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monogenic
monogenic, a. (mɒnəʊˈdʒɛnɪk) [f. Gr. µόνο-ς mono- + γέν-ος kind, origin (cf. -gen) + -ic.] 1. Geol. (See quot.) So F. monogénique.1856 Mayne Expos. Lex., Monogenicus, applied to a rock of which all the parts are of the same nature; thus the monogenic gompholite is a calcareous rock in a calcareous c... Oxford English Dictionary
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Monogenic
Monogenic may refer to: Monogenic signal, in the theory of analytic signals Monogenic disorder, disease, inheritance, or trait, a single gene disorder autosomal dominant gene Monogenic field, in mathematics, an algebraic number field K Monogenic function, a function in an algebra over a field Monogenic wikipedia.org
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Monogenic system
In classical mechanics, a physical system is termed a monogenic system if the force acting on the system can be modelled in a particular, especially convenient The systems that are typically studied in physics are monogenic. wikipedia.org
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Direct product of two finite monogenic semigroup Let $S_1 = \langle a \rangle = M(m_1, r_1) , S_2 = \langle b \rangle = M(m_2, r_2)$ are two finite monogenic semigroup, where $m_1, m_2$ are the index of $S_1,$ $S_2$ a...
It is clear that $\mathbf S_1 \times \mathbf S_2$ is monogenic if either of them is trivial (that is, if either of them has only one element). So, if $\mathbf S_1 \times \mathbf S_2$ were monogenic, it would be generated by $(a,b^s)$ for some $s$.
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Monogenic semigroup
In mathematics, a monogenic semigroup is a semigroup generated by a single element. Monogenic semigroups are also called cyclic semigroups. The monogenic semigroup having index m and period r is denoted by M(m, r). The monogenic semigroup M(1, r) is the cyclic group of order r. wikipedia.org
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Idempotent endomorphism on finite monogenic monoid onto its subgroup Let $S = \langle x ;x^m = x^{m+n} \rangle $ be a monogenic monoid, where $m,n\in\mathbb N$ are least such that $a^m = a^{m+n}$. Then $S$ contains it...
**Hint**. Let $e$ be the idempotent of $G$. Then define $\varphi$ by setting $\varphi(s) = se$.
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Monogenic field
In a monogenic field K, the field discriminant of K is equal to the discriminant of the minimal polynomial of α. While all quadratic fields are monogenic, already among cubic fields there are many that are not monogenic. wikipedia.org
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Ring of integers of simple field extension of local field is monogenic Let $K$ be a local field. Let $\mathcal{O}_K$ be its ring of integers. Let $f(x)\in \mathcal{O}_K[x]$ be monic and irreducible. Consider the exten...
Let $O_K$ be a complete DVR with finite residue field $O_K/(\pi_K)=\Bbb{F}_q$, let $L/K$ a finite extension, $O_L/(\pi_L) = \Bbb{F}_{q^f}$. The valuation extends uniquely to $O_L$, by Hensel lemma $\zeta_{q^f-1} \in O_L$. The ramification index is $e= v(\pi_K)/v(\pi_L)$. $O_L$ is complete, its compl...
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Monogenic function
A monogenic function is a complex function with a single finite derivative. Furthermore, a function which is monogenic , is said to be monogenic on , and if is a domain of , then it is analytic as well (The notion of domains wikipedia.org
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Name for a matrix similar to a companion matrix? Translating "Monogène" matrix from French I am currently translating a research paper from French (which I do not speak well). I have made good progress with copious us...
Such a matrix is said to be _non-derogatory_ in English. The condition is equivalent to one of * having equal minimal and characteristic polynomials, * having a cyclic vector, * being similar to a companion matrix.
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Constructing a new monogenic extension of fields Let $K / F$ and $L / F$ be two extension of fields, where $K / F$ is furthermore monogenic, such that $K$ and $L$ are isomorphic (as fields). Can I state that $L / F$ i...
is a field of rational functions in infinitely many variables, then the fields of rational functions $K=F(Y)$ and $L=F(Y,Z)$ are isomorphic but $K$ is monogenic
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单基因病的遗传模式(孟德尔遗传和非孟德尔遗传) - UpToDate
非孟德尔遗传的原因 常染色体隐性遗传病杂合子的轻度疾病表现 外显率和表现度 不完全或可变外显率 可变表现度 不完全外显和表现度可变的原因 基因多效性 遗传早现
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Find a so that $f$ is not holomorphic Let $f:\Bbb C$ $\rightarrow \Bbb C,$ $f(z)=z^2+a\overline z^2 + 4z\overline z+2z-8\overline z+1+2i$ Find $ a\in \Bbb C$ such that $f$ is not monogenic in any point. From my und...
Write $z = x + iy$. We want to find $a$ such that $2a(x - iy) + 4(x + iy) - 8$ is _never_ zero. Looking separately at the real and imaginary parts, this happens if we never simultaneously have $2ax + 4x - 8 = 0$ and $-2ay + 4y = 0$. The second equation is easily satisfiable regardless of $a$, by jus...
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Find $y \in K$, with $K = F(y)$, such that $y^3 \in F$. Let $K / F$ be a monogenic extension of fields such that the characteristic of $F$ is not $3$ and $[K : F] = 3$. Can I find $y \in K$, with $K = F(y)$, such that...
All finite extensions in characteristic zero are monogenic. This extension is totally real, and of degree three. A monogenic (pure) cubic extension of $\Bbb Q$ has the form $\Bbb Q(\sqrt[3]a)$ and is not totally real.
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Reference for Dedekind's Example of a Non-monogenic Field An oft quoted fact is that Dedekind discovered that adjoining a root of $x^3-x^2-2x-8$ to $\mathbb{Q}$ yields a number field that is not monogenic. Does anyone...
It can be found e.g. in his announcement of the second edition of Dirichlet's Lectures in Number Theory (Gött. gelehrte Anzeigen 1871, 1481--1494; see Dedekind Werke, vol III, p. 406). He published the details in _Über den Zusammenhang zwischen der Theorie der Ideale und der Theorie der höheren Kong...
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