### Table 1. Ore algebras

1996

"... In PAGE 4: ...elds. We specify commutative ring or commutative eld when necessary. Moreover, all rings under consideration in this paper are of characteristic 0. Table1 gives examples of the type of operators we consider. All these operators share a very simple commutation rule of the variable @ with polynomials in x.... In PAGE 5: ...3 Examples of skew polynomial rings are given in Table1 . In all the cases under consideration in this table, A is of either form K[x] or K(q)[x] with K a eld.... In PAGE 6: ...lgebra F of functions, power series, sequences, distributions, etc. Then Eq. (1) extends to the following Leibniz rule for products 8f; g 2 F @i(fg) = i(f)@i(g) + i(f)g: (6)This makes F an S-algebra. The actions of the operators corresponding to important Ore algebras are given in Table1 . In the remainder of this article, we use the word \function quot; to denote any object on which the elements of an Ore algebra act.... In PAGE 8: ... Then O is left Noetherian and a non-commutative version of Buchberger apos;s algorithm terminates. As can be seen from Table1 , this theorem implies that many useful Ore algebras are left Noe-... In PAGE 12: ... Then the annihilating ideal for any product fg where f is annihilated by I and g is annihilated by K is also @- nite. As can be seen from Table1 , this hypothesis does not represent a severe restriction on the class of Ore algebras we consider. Again, f and g in this lemma need not be interpreted as functions but as generators of the O-mod-... ..."

### Table 5: Qualitative influences: non-commutative, associative operators. Sign

2005

Cited by 5

### Table 5 Qualitative influences: non-commutative, associative operators

2004

### Table 1. Canonical forms of geometric algebras Algebras

1998

"... In PAGE 15: ...oordinates, and pi(i=1..n) are points. Similarly, we may define canonical forms in Table1 for all the members of the geometric algebras. Table 1.... ..."

Cited by 4

### Table 10: Signs of additive synergies for the non-commutative, associative operators. Operator Sign

2005

Cited by 5

### Table 10 Signs of additive synergies for the non-commutative, associative oper- ators

2004

### Table 1: Hopf algebras.

2002

"... In PAGE 26: ... A Hopf algebra is a k-vector space, H, equipped with an algebra structure, a com- patible coalgebra structure (= bialgebra) and an antipode satisfying the appropriate equations. Table1 summarizes the necessary structure [29]. We say a Hopf algebra is (co)commutative if the (co)multiplication is (co)commutative, i.... ..."

Cited by 2

### Table 3: The algebra BZ

"... In PAGE 5: ... (1994). As a final example we look at the relation algebra BZ generated by the natural order of an atomless Boolean algebra BU with the extreme elements removed ( Table3 ); we let C8 BPAK and C8C8 BPAC.Observe that BWBW is Boolean complementation.... ..."