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Aperiodic semigroup

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251: 128:, consisting of an identity element and two right zeros. The two-sided Krohn–Rhodes theorem alternatively characterizes finite aperiodic monoids as divisors of iterated block products of copies of the 292: 285: 224: 316: 278: 175: 146: 125: 102: 168:
Monoids, Acts and Categories: With Applications to Wreath Products and Graphs. A Handbook for Students and Researchers
129: 311: 117: 91: 83: 141: 106: 220: 171: 258: 230: 181: 110: 234: 185: 98: 262: 213: 121: 71: 170:. De Gruyter Expositions in Mathematics. Vol. 29. Walter de Gruyter. p. 29. 305: 250: 198:
SchĂĽtzenberger, Marcel-Paul, "On finite monoids having only trivial subgroups,"
17: 25: 75: 40: 59: 219:. Progress in Theoretical Computer Science. Basel: Birkhäuser. 90:-relation is trivial. These two characterizations extend to 166:
Kilp, Mati; Knauer, Ulrich; Mikhalev, Alexander V. (2000).
31:
such that every element is aperiodic, that is, for each
266: 215:
Finite automata, formal logic, and circuit complexity
86:, a finite semigroup is aperiodic if and only if its 212: 120:is that every finite aperiodic monoid divides a 78:, so a synonym used (only?) in such contexts is 286: 8: 293: 279: 158: 58:is an aperiodic semigroup which is a 7: 247: 245: 14: 202:, Vol 8 No. 2, pp. 190–194, 1965. 97:A celebrated result of algebraic 249: 70:A finite semigroup is aperiodic 126:three-element flip-flop monoid 1: 147:Special classes of semigroups 265:. You can help Knowledge by 105:asserts that a language is 66:Finite aperiodic semigroups 333: 244: 211:Straubing, Howard (1994). 103:Marcel-Paul SchĂĽtzenberger 74:it contains no nontrivial 113:is finite and aperiodic. 39:there exists a positive 200:Information and Control 130:two-element semilattice 317:Abstract algebra stubs 261:-related article is a 92:group-bound semigroups 116:A consequence of the 118:Krohn–Rhodes theorem 80:group-free semigroup 142:Monogenic semigroup 109:if and only if its 22:aperiodic semigroup 274: 273: 124:of copies of the 84:Green's relations 324: 312:Semigroup theory 295: 288: 281: 259:abstract algebra 253: 246: 238: 218: 203: 196: 190: 189: 163: 111:syntactic monoid 56:aperiodic monoid 332: 331: 327: 326: 325: 323: 322: 321: 302: 301: 300: 299: 242: 227: 210: 207: 206: 197: 193: 178: 165: 164: 160: 155: 138: 99:automata theory 68: 12: 11: 5: 330: 328: 320: 319: 314: 304: 303: 298: 297: 290: 283: 275: 272: 271: 254: 240: 239: 225: 205: 204: 191: 176: 157: 156: 154: 151: 150: 149: 144: 137: 134: 122:wreath product 82:. In terms of 72:if and only if 67: 64: 13: 10: 9: 6: 4: 3: 2: 329: 318: 315: 313: 310: 309: 307: 296: 291: 289: 284: 282: 277: 276: 270: 268: 264: 260: 255: 252: 248: 243: 236: 232: 228: 226:3-7643-3719-2 222: 217: 216: 209: 208: 201: 195: 192: 187: 183: 179: 173: 169: 162: 159: 152: 148: 145: 143: 140: 139: 135: 133: 131: 127: 123: 119: 114: 112: 108: 104: 100: 95: 93: 89: 85: 81: 77: 73: 65: 63: 61: 57: 53: 49: 45: 42: 38: 34: 30: 27: 23: 19: 267:expanding it 256: 241: 214: 199: 194: 167: 161: 115: 96: 87: 79: 69: 55: 51: 47: 43: 36: 32: 28: 21: 15: 18:mathematics 306:Categories 235:0816.68086 186:0945.20036 177:3110812908 153:References 46:such that 107:star-free 76:subgroups 26:semigroup 136:See also 101:due to 41:integer 233:  223:  184:  174:  60:monoid 54:. An 257:This 24:is a 20:, an 263:stub 221:ISBN 172:ISBN 231:Zbl 182:Zbl 35:in 16:In 308:: 229:. 180:. 132:. 94:. 62:. 50:= 294:e 287:t 280:v 269:. 237:. 188:. 88:H 52:x 48:x 44:n 37:S 33:x 29:S

Index

mathematics
semigroup
integer
monoid
if and only if
subgroups
Green's relations
group-bound semigroups
automata theory
Marcel-Paul SchĂĽtzenberger
star-free
syntactic monoid
Krohn–Rhodes theorem
wreath product
three-element flip-flop monoid
two-element semilattice
Monogenic semigroup
Special classes of semigroups
ISBN
3110812908
Zbl
0945.20036
Finite automata, formal logic, and circuit complexity
ISBN
3-7643-3719-2
Zbl
0816.68086
Stub icon
abstract algebra
stub

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