# Tagged Questions

I've got a couple of things to test against normality in cancellative semigroups. A normal semigroup $S$ is one in which for any $x\in S$ we have $xS=Sx.$ This implies the Ore condition $$x,y\in ... 2answers 195 views ### How much information does the multiplicative semigroup of an algebra contain? How much do we know about an given algebra when we only know its semigroup strucure under the product law? How far can two algebras be distinguished by knowing only their semigroup strucure? The ... 1answer 180 views ### Proving that a semigroup is regular In a number of diverse situations of interest to me (mostly associated with something called the abelian sandpile model), one can define a nonabelian semigroup generated by commuting elements ... 1answer 350 views ### Automorphisms of P(\Bbb N) I believe I've proved that the power semigroup of non-negative integers with addition has a trivial automorphism group. The proof is a bit long, completely elementary and rather unremarkable (as the ... 1answer 124 views ### Idempotents in Green J classes I recently read this article Syntactic semigroups. In page 8, he speaks about a J class having an idempotent is called regular: A \mathcal J-class containing an idempotent is called regular. ... 2answers 205 views ### For a monoid with zero M, how many additive operations on M can there be making M a ring? Let (M,\times) be a monoid with zero. Let \Sigma(M,\times) be the set of binary operations + on M such that (M,+,\times) is a ring. Let \sim be an equivalence relation on ... 1answer 90 views ### What are the semigroups in which congruence classes can be multplied like sets? For a semigroup S and a congruence \rho on S, let's say that \rho is good when for all a,b\in S we have that [ab]=[a][b], where [x] denotes the congruence class of x modulo \rho and ... 4answers 284 views ### On the notion of partial semigroup A partial binary operation on a set X is just a (partial) function \varphi: X \times X \rightharpoonup X (I'm using \rightharpoonup for partial maps), and a partial magma is a pair \mathbb M = ... 2answers 248 views ### What are the monoids in which every globally idempotent subsemigroup contains the identity element? A semigroup is called globally idempotent when for any x\in S there are y,z\in S such that x=yz. Is there a name for monoids whose every globally idempotent subsemigroup contains the identity ... 1answer 152 views ### When does a power semigroup have a zero, and what can the zero be? Let S be a semigroup. The power semigroup of S is the set P(S)=2^S\setminus\lbrace\varnothing\rbrace  with the operation$$AB=\lbrace ab\ |\ a\in A,\ b\in B\rbrace.$$This operation is ... 1answer 209 views ### Embedding Semigroups in Rings Let S be a finite commutative semigroup with identity. Under what conditions (on the semigroup S) it is possible to find a ring R such that the multiplicative structure of R - \{0\} is ... 1answer 191 views ### Is the universal inverse semigroup of a commutative semigroup an embedding? The question of existence of a universal inverse semigroup of an arbitrary semigroup has been answered before (this is a construction similar to the Grothendieck group). Let's refer to the universal ... 2answers 331 views +50 ### Is the class of inverse semigroups globally determined? This question is a follow-up to this one I asked on math.stackexchange. I've decided to ask here because I believe this is a research-level question. I'm sorry if I'm wrong -- I'm not a researcher ... 2answers 414 views ### subsets of \mathbb{R}^+ closed under addition No one's answered this question so here's a simpler question: Has anyone described or catalogued all sets of non-negative real numbers that are closed under addition? In particular, how about those ... 3answers 561 views ### What is the smallest variety of algebras containing all fields? A field is a ring whose nonzero elements form a commutative group under multiplication. A field is also a commutative inverse semigroup with respect to multiplication. The unique multiplicative ... 1answer 411 views ### Magma “actions” (or alternatively, “What is the Yoneda lemma for magmas?”) Arguably the most import thing about groups, semigroups and more generally categories, is that they can act on sets (or even collections of sets in the case of a category). This is the basis for all ... 2answers 440 views ### Do all finitely generated nilpotent semigroups have polynomial growth? The notion of nilpotency passes nicely from groups to semigroups. Define q_1(x,y)=xy and$$q_{i+1}(x,y,z_1,\cdots,z_i)=q_i(x,y,z_1,\cdots,z_{i-1})z_iq_i(y,x,z_1,\cdots,z_{i-1}) inductively for all ...
Suppose that $A_1, \dots, A_k \in M_n(\mathbb{Q})$ and $S$ is the semigroup generated by them. Two questions: are there always a finite set of relations $\{R_i\}$ among the $A_j$ such that $S$ is ...