41. In mathematics, an "'endomorphism "'is a morphism ( or homomorphism ) from a mathematical object to itself. 42. When the field is not algebraically closed, the case where the endomorphism ring is as small as possible is still of particular interest. 43. For each " j ", such that the resulting maps on endomorphism of the elliptic complex " T ". 44. The endomorphism algebra of a tilting module over a hereditary finite dimensional algebra is called a "'tilted algebra " '. 45. In essence, the most general form of a ring, is the endomorphism group of some abelian " X "-group. 46. Non-commutative local rings arise naturally as endomorphism rings in the study of length and is indecomposable, then its endomorphism ring is local. 47. Non-commutative local rings arise naturally as endomorphism rings in the study of length and is indecomposable, then its endomorphism ring is local. 48. More generally, endomorphism rings of abelian groups are rarely commutative, the simplest example being the endomorphism ring of the Klein four-group. 49. More generally, endomorphism rings of abelian groups are rarely commutative, the simplest example being the endomorphism ring of the Klein four-group. 50. A " difference ring " is a commutative ring R together with a ring endomorphism \ sigma \ colon R \ to R.
