...lly in the meaning of [[Von Neumann algebra|von Neumann algebra]] or $W^*$-algebra.
2) A [[Ring with operators|ring with operators]].
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...mple of an non-associative commutative ring is a Jordan ring (see [[Jordan algebra]]).
[[Category:Algebra]]
293 bytes (40 words) - 20:57, 2 November 2014
...e algebra over a field possessing a unit element is imbeddable in a simple algebra with the same unit element.
For references, see [[Simple ring]].
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...ar-algebra(2)|linear algebra]], [[multilinear algebra]], and [[topological algebra]].
An [[algebraic system]], consisting of a set with a family of algebraic operations.
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The centre of a ring $R$ is
the collection $Z$ of all elements of the ring $R$ that commute with every
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''unitary ring, ring with identity, ring-with-a-one''
...ltiplication $(m,r) \cdot (n,s) = (mn, ms + nr + rs)$ which has $(1,0)$ as a multiplicative identity.
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...erfect]]. A [[Noetherian ring|Noetherian]] balanced ring is an [[Artinian ring]].
<TR><TD valign="top">[1]</TD> <TD valign="top"> ''Itogi Nauk. i Tekhn. Algebra Topol. Geom.'' , '''19''' (1981) pp. 31–134</TD></TR>
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...ing|ring]] which is a left (right) [[Semi-chain module|semi-chain module]] over itself.
...e of a serial ring is the ring of formal power series in one variable over a field.
525 bytes (83 words) - 17:14, 7 February 2011
...trass rings are [[analytic ring]]s (rings of convergent power series) over a perfect field, to which the [[Weierstrass preparation theorem]] is applicab
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''with respect to a radical $r$''
...ebras]]; [[Jordan algebra|Jordan algebra]]; [[Lie algebra, semi-simple|Lie algebra, semi-simple]]).
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A ring with division is a (not necessarily associative) [[ring]] in which the equations
$$a \cdot x = b \quad;\quad\quad y \cdot a = b $$
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...operator ring]], when the domain of operators is a commutative associative ring with unit.
...onal vector spaces and linear operators between them. See the entry Linear algebra below.
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...acobson ring. On the contrary, a local non-Artinian ring is not a Jacobson ring.
...o the spectrum $\mathrm{Spec}(A)$; this definition leads to the concept of a Jacobson scheme.
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...full matrix ring of a [[local ring]]. This holds, in particular, if $J$ is a [[nil ideal]].
<TR><TD valign="top">[2]</TD> <TD valign="top"> C. Faith, "Algebra" , '''1–2''' , Springer (1973–1976)</TD></TR>
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...e additive group of $B$ and for which $(ab)\phi=b\phi\cdot a\phi$ ($a,b\in A$).
The [[opposite ring]] $R^{\mathrm{op}}$ to a ring $R$ is anti-isomorphic to $R$.
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...e. $\partial(\alpha x) = \alpha \partial(x)$, where $\alpha \in K$, $x \in A$.
Cf. also [[Derivation in a ring]].
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''$M$ over a commutative ring $R$''
.... For example, for a finite Abelian group$M$ regarded as a module over the ring of integers, $\mathrm{Supp}(M)$ consists of all prime ideals $(p)$, where $
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The term ''regular algebra'' may refer to:
* a [[regular ring (in commutative algebra)]];
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...he first one is. Every automorphism of a finite-dimensional central simple algebra is inner and its dimension is the square of an integer.
...="top">[2]</TD> <TD valign="top"> L.A. Skornyakov, "Elements of general algebra" , Moscow (1983) (In Russian)</TD></TR>
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...o be strongly degenerate. The smallest ideal of a Lie algebra the quotient algebra by which is not strongly degenerate is called the Kostrikin radical.
...60 (In Russian)</TD></TR><TR><TD valign="top">[3]</TD> <TD valign="top"> A.I. Kostrikin, "Around Burnside" , Springer (1989) (Translated from Russ
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