A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
On maximal orders of division quaternion algebras over the rational number field with certain optimal embeddings

1982
*
Nagoya mathematical journal
*

In this paper, we shall give explicitZ-basis

doi:10.1017/s002776300002016x
fatcat:brw3uajhz5d4vbv3yc7fhanvjm
*of*certain maximal*orders**of*definite quaternion algebras over the*rational*number fieldQ(See Theorems below). ... We shall also give some remarks on symmetric maximal*orders*in Ponomarev [9] and Hashimoto [6] (Proposition 4.3). More precise contents are as follows. LetDbe a*division*quaternion algebra overQ. ... Besides, when m = 3 mod 4, we choose a*rational*integer r r such that ( 4) r' 2 + m = 0 mod 4<? . Put θ = Z + Z-ii^-+ Z/3 + Z (r ' + a)β . 2 2g Then, this is also a maximal*order**of*D. ...##
###
Page 171 of American Mathematical Society. Transactions of the American Mathematical Society Vol. 13, Issue 2
[page]

1912
*
American Mathematical Society. Transactions of the American Mathematical Society
*

Now suppose, if possible, that there exists an integral

*rational*function G, (2, v) which is not*divisible*by z — a, and which possesses y,, uw, -**, H, as its*orders**of*coincidence with the branches*of*... By repeated applications*of*the above process, it would evidently be possible to construct an integral*rational*function G (z, 7), which is not*divisible*by z — a, and whose*orders**of*coincidence with ...##
###
Page 4 of The Month Vol. 28, Issue 148
[page]

1876
*
The Month
*

Defi- nition

*of*Philosophy.*Divisions*. Logic. Zhe First Part.—On the efficient cause*of*the*Rational**Order*. Lecture III. The Efficient Cause*of*the*Rational**Order*. Zhe Second Part. ... —On the material cause*of*the*Rational**Order*. Lecture IV. Definitions and*Divisions**of*Terms. Lecture V. On Definition and*Division*. Lecture VI. On the Definition and*Division**of*Propositions. ...##
###
c-Orderable division rings with involution

1982
*
Journal of Algebra
*

Another important property

doi:10.1016/0021-8693(82)90053-9
fatcat:5zmz3pjtcbcg3jjfjdbit4hopi
*of*the c-*ordering*is that the set*of*bounded elements x at this*ordering*(e.g., XX* < rO for some*rational*r") is a *-valuation subring Y ... In fact, any c-*orderable**division*ring R is shown to admit an*ordering**of*the following type. ... In fact, any c-*orderable**division*ring R is shown to admit an*ordering**of*the following type. ...##
###
Divisibility Monoids: Presentation, Word Problem, and Rational Languages
[chapter]

2001
*
Lecture Notes in Computer Science
*

Essentially, Theorem 13 says that a

doi:10.1007/3-540-44669-9_23
fatcat:t3e5knp7bvfbxowdzhurbfxxhq
*divisibility*monoid satisfies Kleene's Theorem if and only if it is*rational*if and only if it is width-bounded. Thus, in the context*of**divisibility*monoids, ... It turns out that this is the case iff the*divisibility*monoid is a*rational*monoid [25] iff it is width-bounded. ...*Ordered*monoids where the*order*relation is the intersection*of*the prefix and the suffix relation were investigated e.g. in [2] under the name "*divisibility*monoid". ...##
###
Quaternion constituents of group algebras

1971
*
Proceedings of the American Mathematical Society
*

In this paper it is shown that each quaternion

doi:10.1090/s0002-9939-1971-0280609-0
fatcat:gc5oixk6kjdaxmfgqoktrmixxa
*division*algebra central over the*rationals*appears as a*division*ring constituent*of*some*rational*group algebra. ... For*rational**division*algebras, the Hasse invariants correspond to the set*of**rational*primes including the infinite prime. ... Let A be a cyclic group*of**order*p, T cyclic*of**order*2n+1, and M cyclic*of**order*m. Set G = A(TXM), the semidirect product with A <JG and |GTAfG4)|=2. ...##
###
The Cyclic Group as a Basic Element in the Theory of Numbers

1911
*
The American mathematical monthly
*

is

doi:10.1080/00029890.1911.11997639
fatcat:266vnpitq5dgxhjjinmvxvbkay
*divisible*by the*rational*integer m. ... The term*order**of*a*rational*integer a with respect to modulus m, m being a positive*rational*integer, will be used for the smallest positive*rational*integer b which is such that the product ab is*divisible*...##
###
The Cyclic Group as a Basic Element in the Theory of Numbers

1911
*
The American mathematical monthly
*

The term

doi:10.2307/2972576
fatcat:ddoferkblvaubo7i3fmvopyope
*order**of*a*rational*integer a with respect to modulus m, mn being a positive*rational*integer, will be used for the smallest positive*rational*integer b which is such that the product ab is*divisible*... This proves the theorem: If paiS the highest power*of*a*rational*prime number which divides the*order*(mod m)*of*one*of*two*rational*integers without dividing this*order**of*the other, then the*order*(mod ...##
###
Page 493 of American Mathematical Society. Transactions of the American Mathematical Society Vol. 97, Issue 3
[page]

1960
*
American Mathematical Society. Transactions of the American Mathematical Society
*

Clearly the character group

*of*X contains no elements*of*finite*order*since X is*divisible*. ... Since H’ CH, H(\K =0, K has no nontrivial elements*of*finite*order*and consequently K is a vector space over the*rational*numbers [4, p. 10]. ...##
###
ON NORMAL SUBGROUPS OF D∗ WHOSE ELEMENTS ARE PERIODIC MODULO THE CENTER OF D∗ OF BOUNDED ORDER

2014
*
International Electronic Journal of Algebra
*

Let D be a

doi:10.24330/ieja.266227
fatcat:pbepn5a2kfct7osqadejhyp6va
*division*ring with the center F = Z(D). ... Suppose that N is a normal subgroup*of*D * which is radical over F , that is, for any element x ∈ N , there exists a positive integer nx, such that x nx ∈ F . ... ON NORMAL SUBGROUPS*OF*D * ...##
###
Primitive Points on Elliptic Curves
[chapter]

2000
*
Springer Collected Works in Mathematics
*

Our purpose here is to formulate an analogous conjecture on elliptic curves A, say defined over the

doi:10.1007/978-1-4614-8710-4_19
fatcat:mf67jsvjdzev3bznyajaeu2pii
*rationals*for concreteness. Let a be a*rational*point*of*infinite*order*. ... Note that / divides the*order**of*-4(F) if and only if 7 p has eigenvalue 1. Furthermore, A(F ) = Ker (7 -1). If y p = 1 then the index*of*(a) is*divisible*by /. ... Our purpose here is to formulate an analogous conjecture on elliptic curves A, say defined over the*rationals*for concreteness. Let a be a*rational*point*of*infinite*order*. ...##
###
Primitive Points on Elliptic Curves
[chapter]

2000
*
Collected Papers Volume II
*

Our purpose here is to formulate an analogous conjecture on elliptic curves A, say defined over the

doi:10.1007/978-1-4612-2120-3_19
fatcat:zjjyj5hz5nbh5ccb6cd25r7mbq
*rationals*for concreteness. Let a be a*rational*point*of*infinite*order*. ... Note that / divides the*order**of*-4(F) if and only if 7 p has eigenvalue 1. Furthermore, A(F ) = Ker (7 -1). If y p = 1 then the index*of*(a) is*divisible*by /. ... Our purpose here is to formulate an analogous conjecture on elliptic curves A, say defined over the*rationals*for concreteness. Let a be a*rational*point*of*infinite*order*. ...##
###
Primitive points on elliptic curves

1977
*
Bulletin of the American Mathematical Society
*

Our purpose here is to formulate an analogous conjecture on elliptic curves A, say defined over the

doi:10.1090/s0002-9904-1977-14310-3
fatcat:wzc5iumcabdapoz7pm5t6xxypq
*rationals*for concreteness. Let a be a*rational*point*of*infinite*order*. ... Note that / divides the*order**of*-4(F) if and only if 7 p has eigenvalue 1. Furthermore, A(F ) = Ker (7 -1). If y p = 1 then the index*of*(a) is*divisible*by /. ... Our purpose here is to formulate an analogous conjecture on elliptic curves A, say defined over the*rationals*for concreteness. Let a be a*rational*point*of*infinite*order*. ...##
###
Page 621 of Annals of Mathematics Vol. 30, Issue
[page]

1928
*
Annals of Mathematics
*

THE STRUCTURE

*OF*ANY ALGEBRA WHICH IS A DIRECT PRODUCT*OF**RATIONAL*GENERALIZED QUATERNION*DIVISION*ALGEBRAS.* By A. ADRIAN ALBERT. 1. Introduction. ... The direct products*of*two generalized quaternion*division*algebras over R. We shall consider*rational*linear associative algebras, , that is algebras over R, the field*of*all*rational*numbers. ...##
###
On Division Algebras

1921
*
Transactions of the American Mathematical Society
*

If B is a subalgebra

doi:10.2307/1989011
fatcat:hpku6ograbck7g5x2m3pp6f2tu
*of**order*b in a*division*algebra A*of**order*a, there exists a complex C*of**order*c such that A = BC, a = 6c. ... It is shown in the present paper that the Dickson algebra is the only noncommutative algebra*of**order*9 so that the only*division*algebras*of**order*not greater than 9 are (i) the Dickson algebras*of**order*... If B is a subalgebra*of**order*b in a*division*algebra A*of**order*a, there exists a complex C*of**order*c such that A = BC, a = 6c. ...
« Previous

*Showing results 1 — 15 out of 418,638 results*