All Questions
Tagged with ra.rings-and-algebras universal-algebra
69 questions
3
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0
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95
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Lie structure over $R$-module
In Higgins' paper Baer invariants and the Birkhoff-Witt theorem (J. Algebra 11 (1969) 469–482, doi:10.1016/0021-8693(69)90086-6) the following definition is given:
A Lie structure over the $R$-module ...
- 427
3
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0
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79
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Semigroups containing an ideal with a local identity
I'm looking for some classes of semigroups containing a (proper) ideal with a local identity (i.e., ideal submonoid). Can somebody give some examples or/and theorems for the followings cases:
(a) ...
- 995
2
votes
1
answer
195
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Cyclic Distribution on the reals?
Do there exist binary operators *, **, and *** on the real numbers, such that ...
- 21
2
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1
answer
260
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Universal constructions that factor through endomorphisms
If $\cal A$ is a variety of algebras (e.g., all groups) and $\cal B$ is a subvariety defined by some set of identities $X$ (e.g., abelian groups with $X = \{xy \simeq yx\}$), then there is a functor $...
- 879
2
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1
answer
197
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Varieties of rational languages and (pseudo-)varieties of finite monoids, question regarding closure property
Let $\mathcal Rat(A)$ denote the class of rational (or regular) languages over the alphabet $A$, a subset $\mathcal V(A) \subseteq \mathcal Rat(A)$ is called a variety of (rational) languages iff
...
- 798
2
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1
answer
111
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Algebras determined by their globals
If $A= (A, f_1, f_2, ...f_n)$ is an algebra, then its global (sometimes referred to as complex algebras) $\mathcal{U}(A)$ is defined on the power set $\wp(A)$ in the usual way.
It is known that $\...
- 161
2
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1
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211
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Terminology for a monoid $(H, \cdot)$ s.t. $ax=a$ or $xa =a$ only if $x$ is a unit
Let $(H, \cdot)$ be a (multiplicative) monoid. Is there any consolidated name for the following Property $\text{(P)}$, or for the class of monoids for which it is satisfied?
$$\text{(P) If }\,xy = x\...
- 10.5k
2
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0
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81
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The involutive structure on a division ring
This question is motivated by foundations of geometry, namely, by studying scalars in affine spaces.
Let $F$ be a field (or better a division ring). It has the operations of addition and ...
- 41.9k
2
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0
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286
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Union star symbol in set theory
In the slides Provenance for Database Transformations, page 24, they provide a semiring for lineage, which include a $\cup^*$ symbol. However, I can not find any related materials about the meaning of ...
2
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0
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169
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What is the difference between a monosemiring and a semigroup?
What is the difference between a monosemiring and a semigroup?
The following definitions are for clarity of my question.
A semigroup $S$ is a non empty set that satisfies closure and associativity ...
- 203
1
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1
answer
215
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Reference about cancellation property for semigroups
Have the semigroups with the following cancellation property been studied?
Property: Let $S$ be a semigroup and $x,y\in S$ such that $xz=yz,$ for all $z\in S,$ then $x=y$.
- 313
1
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1
answer
349
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Lawvere theory of Lawvere theories
There is a coloured operad $sOp$ such that $sOp$-algebras are single-coloured operads. This operad has a simple description in terms of generators and relations, say, as an operad $F(X)/R$. There is a ...
- 103
1
vote
2
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221
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Example of idempotent left quasigroups which are right-distributive but not left-distributive
I am looking for examples of the following algebraic structure: a set (X,.) which satisfy the axioms
(idempotent) x.x = x
(left quasigroup) the equation a.x = b has a unique solution denoted by x = ...
- 785
1
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0
answers
66
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First isomorphism theorem for inverse semigroups together with v-prehomomorphisms?
In this old paper D. B. McAlister has introduced another class of morphisms for inverse semigroups, called v-prehomomorphisms. For such a morphism $\theta : S \to T,$ instead of preserving the ...
- 1,093
1
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0
answers
138
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Is every monosemiring an idempotent semiring?
Is every monosemiring an idempotent semiring?
To make my question clear, let me give definitions as follows:
A semiring $(R, +, .)$ is said to be monosemiring if $x.y= x+y$ for all $x, y$ in $R$. And ...
- 203
0
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1
answer
654
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Book on algebraic structures
What is the most complete book on algebraic structures that deals with the complete taxonomy from magmas to Lie algebras and inner product spaces?
- 19
0
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0
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105
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Definition of term functions, in universal algebra
According to the definitions in Sankappanavar's universal algebra :
Assume $p$ is a term, then $p(x_1,x_2,...,x_n)$ indicates that the variables occurring in $p$ are among $x_1,...,x_n$. But there is ...
- 11
0
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0
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101
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Is a principal filter in a free Heyting algebra a projective Heyting algebra?
A Heyting algebra is a bounded distributive lattice $(L,\vee,\wedge,0,1)$ together with a binary operation $\rightarrow$ called implication or relative pseudocomplementation with the property that, ...
- 1,644
-2
votes
1
answer
131
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SHPS and SPHS inequality using monounary algebra
Let $A_n = \{(1,\ldots,n) , f \}$ where $f(i) = (i+1)$ if $i \neq n $ otherwise $f(n) = 1$.
This describes a mono unary algebra.
The proof for $HPS \neq SPHS$ I know uses metabelian groups and was ...
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