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syzygy

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syzygy
syzygy (ˈsɪzɪdʒɪ) Also 7 sys-, syzigie, 7–8 sys-, syzygie, 8–9 syzigy, 9 syzigee. [ad. late L. sȳzygia, a. Gr. συζυγία yoke, pair, copulation, conjunction, f. σύζυγος yoked, paired, f. σύν syn-1 + ζυγ-: ζευγνύναι to yoke. Cf. F. syzygie (1584 in Hatz.-Darm.).] 1. Astron. † a. Orig. = conjunction 3. ... Oxford English Dictionary
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Syzygy
Syzygy (mathematics), linear relation between generators of a module Syzygy, in biology, the pairing of chromosomes during meiosis Syzygy endgame tablebases Coney Syzygy (novel), a novel by Frederik Pohl Syzygy (poetry), the combination of two metrical feet into a single unit Syzygy Darklock, a fictional wikipedia.org
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Syzygy (astronomy)
Solar and lunar eclipses occur at times of syzygy, as do transits and occultations. Tidal variation A syzygy causes the fortnightly phenomena of spring and neap tides. At the new and full moon, the Sun and Moon are in syzygy. wikipedia.org
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7-piece Syzygy tablebases are complete - lichess.org
Congratulations to Bojun Guo (aka noobpwnftw) and Ronald de Man (aka syzygy) for completing the first free 7-piece tablebase and generously sharing it with the world! Lichess now provides online access on the analysis board and in studies, practice against tablebases, a public API and a mirror for downloading the full tablebase files.
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Projective syzygy vs. free syzygy When referring to syzygies, some books refer to free resolution and some books refer to projective resolution. Are they equivalent in some sense? Is it true, for instance, that the $n...
No. A module can have different projective and free dimensions. Very nice examples can be found here. The free dimension of a projective module can be as big as one. If the ring satisfies some hypotheses, then the answer becomes yes. For example, over a local commutative ring, or a non-negatively gr...
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Syzygy (poetry)
In poetry, a syzygy is the combination of two metrical feet into a single unit, similar to an elision. Consonantal or phonetic syzygy is also similar to the effect of alliteration, where one consonant is used repeatedly throughout a passage, but not necessarily wikipedia.org
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Generalizations of Hilbert's Syzygy theorem Hilbert's Syzygy theorem states that a minimal free resolution of a finitely generated graded module over a (standard graded) polynomial ring in $n$ variables $k[x_1, \ldots...
As suggested by Jason I put my comments into an answer. Hilbert's theorem means that all modules over $k[x_1,\ldots ,x_n]$ have projective dimension $\leq n$ -- one says that the _global dimension_ (aka homological dimension) of $k[x_1,\ldots ,x_n]$ is $n$. This is a property of the ring $k[x_1,\ldo...
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Syzygy (novel)
Syzygy is a 1981 novel by Frederik Pohl. wikipedia.org
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Syzygy (EP)
Syzygy saw the return of original Lynch Mob vocalist Oni Logan, and the departure of Robert Mason. The band broke up again after a single writing session, which resulted in Syzygy. wikipedia.org
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Properties of the first syzygy over Dedekind domains Let $L$ be a Dedekind domain and $I = (a) + (b)$ a non-principal proper ideal in $L$. Consider equation of the form $xa + yb = 0$. Is it true that then there exists...
Let $M\subset L$ be any maximal ideal. We will show that there exists $x,y\in L$ with $xa+yb=0$ and $(x,y)$ is not contained in $M$, which will show that no such proper ideal $J$ as in your question exists. If you localize at $M$, then $L_M$ is a pid and thus $(a,b)$ is principal, generated by eithe...
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Syzygy (The X-Files)
"Syzygy" is the thirteenth episode of the third season of the science fiction television series The X-Files. "Syzygy" earned a Nielsen household rating of 10.8, being watched by 16.04 million people in its initial broadcast. wikipedia.org
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Hilbert Syzygy Theorem for non-graded modules The statement of Hilbert Syzygy Theorem is as follows: Let $R = k[x_1 , \ldots , x_n]$ be a polynomial ring over a field $k$ and $M$ be a finitely generated graded $R$-mod...
That is correct. Actually, the modern statement of this theorem is that any polynomial ring $k[X_1,\dots,X_n]$ over a field $k$ has _global homological dimension_ equal to $n$.
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Existence of Hilbert's polynomial I heard that Hilbert's syzygy theorem can be used to show the existence of Hilbert polynomials. How does the construction works? Namely, why do every coherent $O$-module $\mathscr F$ ...
You know the cohomology groups of $\mathscr{O}_{\mathbf{P}^n}(m)$, so compute $\chi(\mathscr{O}_{\mathbf{P}^n}(m))$ and show that the result is a polynomial in $m$. Then you probably need to recall or prove the fact that if $$0 \to \mathscr{F}_1 \to \cdots \to \mathscr{F}_n \to 0$$ is exact then the...
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Hilbert's syzygy theorem
The second syzygy module is the module of the relations between generators of the first syzygy module. th syzygy module of is always a free module. wikipedia.org
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GitHub
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